00444nas a2200133 4500008004100000022001400041245008800055210006900143300001400212490000800226100001900234700002100253856003600274 2018 eng d a0564-616200aDiscriminant circle bundles over local models of Strebel graphs and Boutroux curves0 aDiscriminant circle bundles over local models of Strebel graphs a163–2070 v1971 aBertola, Marco1 aKorotkin, D., A. uhttps://doi.org/10.4213/tmf951300445nas a2200109 4500008004100000245006800041210006800109100001900177700002000196700001600216856010300232 2018 eng d00aNoncommutative Painlevé Equations and Systems of Calogero Type0 aNoncommutative Painlevé Equations and Systems of Calogero Type1 aBertola, Marco1 aCafasso, Mattia1 aRubtsov, V. uhttps://math.sissa.it/publication/noncommutative-painlev%C3%A9-equations-and-systems-calogero-type01284nas a2200145 4500008004100000245008600041210007000127260004400197490000700241520070800248100001900956700003200975700001801007856011301025 2018 eng d00aPainlevé IV Critical Asymptotics for Orthogonal Polynomials in the Complex Plane0 aPainlevé IV Critical Asymptotics for Orthogonal Polynomials in t bNational Academy of Sciences of Ukraine0 v143 a
We study the asymptotic behaviour of orthogonal polynomials in the complex plane that are associated to a certain normal matrix model. The model depends on a parameter and the asymptotic distribution of the eigenvalues undergoes a transition for a special value of the parameter, where it develops a corner-type singularity. In the double scaling limit near the transition we determine the asymptotic behaviour of the orthogonal polynomials in terms of a solution of the Painlev´e IV equation. We determine the Fredholm determinant associated to such solution and we compute it numerically on the real line, showing also that the corresponding Painlev´e transcendent is pole-free on a semiaxis.
1 aBertola, Marco1 aElias Rebelo, José Gustavo1 aGrava, Tamara uhttps://math.sissa.it/publication/painlev%C3%A9-iv-critical-asymptotics-orthogonal-polynomials-complex-plane00428nas a2200109 4500008004100000245009800041210007000139490003400209100001900243700002000262856003600282 2017 eng d00aThe Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes' phenomenon0 aKontsevich matrix integral convergence to the Painlevé hierarchy0 vDOI 10.1007/s00220-017-2856-31 aBertola, Marco1 aCafasso, Mattia uhttp://arxiv.org/abs/1603.0642000364nas a2200121 4500008004100000022001400041245004900055210004500104300002200149490000700171100001900178856004500197 2017 eng d a1815-065900aThe Malgrange form and Fredholm determinants0 aMalgrange form and Fredholm determinants aPaper No. 046, 120 v131 aBertola, Marco uhttp://dx.doi.org/10.3842/SIGMA.2017.04600465nas a2200133 4500008004100000022001400041245009600055210006900151300001400220490000800234100001900242700002200261856004800283 2017 eng d a0010-361600aMaximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation0 aMaximal amplitudes of finitegap solutions for the focusing Nonli a525–5470 v3541 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.1007/s00220-017-2895-900453nas a2200133 4500008004100000245009600041210006900137260000700206300001100213100001900224700002100243700001800264856003700282 2017 eng d00aSymplectic geometry of the moduli space of projective structures in homological coordinates0 aSymplectic geometry of the moduli space of projective structures c06 a1–561 aBertola, Marco1 aKorotkin, Dmitry1 aNorton, Chaya uhttps://arxiv.org/abs/1506.0791800463nas a2200133 4500008004100000022001400041245009600055210006900151300001600220490000600236100001900242700002000261856004800281 2017 eng d a2010-326300aUniversality of the matrix Airy and Bessel functions at spectral edges of unitary ensembles0 aUniversality of the matrix Airy and Bessel functions at spectral a1750010, 220 v61 aBertola, Marco1 aCafasso, Mattia uhttp://dx.doi.org/10.1142/S201032631750010100795nas a2200241 4500008004100000245011200041210006900153260003500222300001100257490000800268100001800276700001800294700001600312700002200328700001900350700002300369700002200392700002200414700001800436700001800454700002100472856006000493 2017 eng d00aUniversality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation0 aUniversality of the Peregrine Soliton in the Focusing Dynamics o bAmerican Physical SocietycJul a0339010 v1191 aTikan, Alexey1 aBillet, Cyril1 aEl, Gennady1 aTovbis, Alexander1 aBertola, Marco1 aSylvestre, Thibaut1 aGustave, Francois1 aRandoux, Stephane1 aGenty, Goëry1 aSuret, Pierre1 aDudley, John, M. uhttps://link.aps.org/doi/10.1103/PhysRevLett.119.03390100479nas a2200133 4500008004100000022001400041245010000055210006900155300002800224490000700252100001900259700002200278856004500300 2016 eng d a1815-065900aOn asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight0 aasymptotic regimes of orthogonal polynomials with complex varyin aPaper No. 118, 50 pages0 v121 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.3842/SIGMA.2016.11800506nas a2200145 4500008004100000022001400041245011400055210006900169300001200238490000800250100001900258700002000277700001300297856005000310 2016 eng d a0167-278900aCorrelation functions of the KdV hierarchy and applications to intersection numbers over $\overline\CalM_g,n$0 aCorrelation functions of the KdV hierarchy and applications to i a30–570 v3271 aBertola, Marco1 aDubrovin, Boris1 aYang, Di uhttp://dx.doi.org/10.1016/j.physd.2016.04.00800358nas a2200097 4500008004100000245008800041210006900129260000700198100001900205856003600224 2016 eng d00aCORRIGENDUM: The dependence on the monodromy data of the isomonodromic tau function0 aCORRIGENDUM The dependence on the monodromy data of the isomonod c011 aBertola, Marco uhttp://arxiv.org/abs/1601.0479000491nas a2200145 4500008004100000022001400041245009400055210006900149300001400218490000700232100001900239700001900258700002000277856004800297 2016 eng d a0176-427600aHankel determinant approach to generalized Vorob'ev-Yablonski polynomials and their roots0 aHankel determinant approach to generalized VorobevYablonski poly a417–4530 v441 aBalogh, Ferenc1 aBertola, Marco1 aBothner, Thomas uhttp://dx.doi.org/10.1007/s00365-016-9328-400485nas a2200145 4500008004100000022001400041245008800055210006900143300001700212490000800229100001900237700001600256700002200272856004500294 2016 eng d a1364-502100aRogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation0 aRogue waves in multiphase solutions of the focusing nonlinear Sc a20160340, 120 v4721 aBertola, Marco1 aEl, Gennady1 aTovbis, Alexander uhttp://dx.doi.org/10.1098/rspa.2016.034000393nas a2200121 4500008004100000245004500041210004500086490000900131100001900140700002000159700001300179856007900192 2016 eng d00aSimple Lie Algebras and Topological ODEs0 aSimple Lie Algebras and Topological ODEs0 v20161 aBertola, Marco1 aDubrovin, Boris1 aYang, Di uhttps://math.sissa.it/publication/simple-lie-algebras-and-topological-odes00430nas a2200109 4500008004100000245006500041210006200106100001900168700002500187700002200212856008600234 2016 eng d00aOn Sobolev instability of the interior problem of tomography0 aSobolev instability of the interior problem of tomography1 aBertola, Marco1 aKatsevich, Alexander1 aTovbis, Alexander uhttps://math.sissa.it/publication/sobolev-instability-interior-problem-tomography00522nas a2200133 4500008004100000022001400041245015400055210006900209300001400278490000700292100001900299700002200318856004800340 2015 eng d a0176-427600aAsymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation0 aAsymptotics of orthogonal polynomials with complex varying quart a529–5870 v411 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.1007/s00365-015-9288-000480nas a2200133 4500008004100000022001400041245011900055210006900174300001500243490000700258100001900265700002200284856004000306 2015 eng d a0022-248800aA degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems0 adegeneration of twophase solutions of the focusing nonlinear Sch a061507, 170 v561 aBertola, Marco1 aGiavedoni, Pietro uhttp://dx.doi.org/10.1063/1.492236200454nas a2200133 4500008004100000022001400041245009000055210006900145300001100214490000600225100001900231700002200250856004800272 2015 eng d a1664-236800aMeromorphic differentials with imaginary periods on degenerating hyperelliptic curves0 aMeromorphic differentials with imaginary periods on degenerating a1–220 v51 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.1007/s13324-014-0088-700453nas a2200133 4500008004100000022001400041245008800055210006900143300001500212490000700227100001900234700001300253856005300266 2015 eng d a1751-811300aThe partition function of the extended $r$-reduced Kadomtsev-Petviashvili hierarchy0 apartition function of the extended rreduced KadomtsevPetviashvil a195205, 200 v481 aBertola, Marco1 aYang, Di uhttp://dx.doi.org/10.1088/1751-8113/48/19/19520500527nas a2200157 4500008004100000022001400041245010200055210006900157300001400226490000700240100001900247700001900266700002000285700002400305856004000329 2015 eng d a0010-364000aStrong asymptotics of the orthogonal polynomials with respect to a measure supported on the plane0 aStrong asymptotics of the orthogonal polynomials with respect to a112–1720 v681 aBalogh, Ferenc1 aBertola, Marco1 aLee, Seung-Yeop1 aMcLaughlin, Kenneth uhttp://dx.doi.org/10.1002/cpa.2154100475nas a2200133 4500008004100000245009800041210006900139260000700208300001600215490000800231100001900239700002000258856006300278 2015 eng d00aUniversality Conjecture and Results for a Model of Several Coupled Positive-Definite Matrices0 aUniversality Conjecture and Results for a Model of Several Coupl c08 a1077–11410 v3371 aBertola, Marco1 aBothner, Thomas uhttp://link.springer.com/article/10.1007/s00220-015-2327-700469nas a2200145 4500008004100000022001400041245007300055210006900128300001400197490000800211100001900219700001700238700002000255856004800275 2014 eng d a0010-361600aCauchy-Laguerre two-matrix model and the Meijer-G random point field0 aCauchyLaguerre twomatrix model and the MeijerG random point fiel a111–1440 v3261 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttp://dx.doi.org/10.1007/s00220-013-1833-800419nas a2200121 4500008004100000245005500041210005500096300000700151490001100158100001900169700002000188856008900208 2014 eng d00aDarboux Transformations and Random Point Processes0 aDarboux Transformations and Random Point Processes a560 vrnu1221 aBertola, Marco1 aCafasso, Mattia uhttps://math.sissa.it/publication/darboux-transformations-and-random-point-processes00577nas a2200109 4500008004100000245016900041210006900210100001900279700002500298700002200323856012200345 2014 eng d00aSingular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach0 aSingular Value Decomposition of a Finite Hilbert Transform Defin1 aBertola, Marco1 aKatsevich, Alexander1 aTovbis, Alexander uhttps://math.sissa.it/publication/singular-value-decomposition-finite-hilbert-transform-defined-several-intervals-and00476nas a2200109 4500008004100000245009100041210006900132490001100201100001900212700002000231856011500251 2014 eng d00aZeros of Large Degree Vorob'ev-Yablonski Polynomials via a Hankel Determinant Identity0 aZeros of Large Degree VorobevYablonski Polynomials via a Hankel 0 vrnu2391 aBertola, Marco1 aBothner, Thomas uhttps://math.sissa.it/publication/zeros-large-degree-vorobev-yablonski-polynomials-hankel-determinant-identity00476nas a2200121 4500008004100000245011700041210006900158300001200227490000700239100001900246700002000265856006900285 2013 eng d00aThe gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation0 agap probabilities of the tacnode Pearcey and Airy point processe a13500030 v021 aBertola, Marco1 aCafasso, Mattia uhttp://www.worldscientific.com/doi/abs/10.1142/S201032631350003200476nas a2200145 4500008004100000022001400041245007100055210006700126300001600193490000800209100001900217700001800236700002200254856005400276 2013 eng d a0002-993900aInversion formulae for the $\romancosh$-weighted Hilbert transform0 aInversion formulae for the romancoshweighted Hilbert transform a2703–27180 v1411 aBertola, Marco1 aKatsevich, A.1 aTovbis, Alexander uhttp://dx.doi.org/10.1090/S0002-9939-2013-11642-400539nas a2200157 4500008004100000022001400041245011800055210006900173300001400242490000800256100001900264700001900283700001600302700001500318856004800333 2013 eng d a0022-471500aSpectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes0 aSpectra of random Hermitian matrices with a smallrank external s a654–6970 v1531 aBertola, Marco1 aBuckingham, R.1 aLee, S., Y.1 aPierce, V. uhttp://dx.doi.org/10.1007/s10955-013-0845-200580nas a2200145 4500008004100000022001400041245010700055210006900162300001500231490000700246100001900253700001700272700002000289856012500309 2013 eng d a0022-248800aStrong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model0 aStrong asymptotics for Cauchy biorthogonal polynomials with appl a043517, 250 v541 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttps://math.sissa.it/publication/strong-asymptotics-cauchy-biorthogonal-polynomials-application-cauchy-two-matrix-model00539nas a2200133 4500008004100000022001400041245017800055210007000233300001400303490000700317100001900324700002200343856004000365 2013 eng d a0010-364000aUniversality for the focusing nonlinear Schrödinger equation at the gradient catastrophe point: rational breathers and poles of the \it Tritronquée solution to Painlevé I0 aUniversality for the focusing nonlinear Schrödinger equation at a678–7520 v661 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.1002/cpa.2144500484nas a2200133 4500008004100000022001400041245009400055210006900149300001400218490000800232100001900240700002000259856007100279 2012 eng d a0010-361600aFredholm determinants and pole-free solutions to the noncommutative Painlevé II equation0 aFredholm determinants and polefree solutions to the noncommutati a793–8330 v3091 aBertola, Marco1 aCafasso, Mattia uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-011-1383-x00466nas a2200121 4500008004100000022001400041245010500055210006900160300001600229490000700245100001900252856007300271 2012 eng d a0951-771500aOn the location of poles for the Ablowitz-Segur family of solutions to the second Painlevé equation0 alocation of poles for the AblowitzSegur family of solutions to t a1179–11850 v251 aBertola, Marco uhttp://0-dx.doi.org.mercury.concordia.ca/10.1088/0951-7715/25/4/117900516nas a2200145 4500008004100000022001400041245008700055210007100142300001600213490000800229653002300237100001900260700002000279856007100299 2012 eng d a0167-278900aRiemann–Hilbert approach to multi-time processes: The Airy and the Pearcey cases0 aRiemann–Hilbert approach to multitime processes The Airy and the a2237 - 22450 v24110aIntegrable kernels1 aBertola, Marco1 aCafasso, Mattia uhttp://www.sciencedirect.com/science/article/pii/S016727891200011500559nas a2200157 4500008004100000022001400041245011500055210006900170300001400239490000800253100001900261700001900280700001600299700001500315856007100330 2012 eng d a0022-471500aSpectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes0 aSpectra of random Hermitian matrices with a smallrank external s a475–5180 v1461 aBertola, Marco1 aBuckingham, R.1 aLee, S., Y.1 aPierce, V. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-200425nas a2200121 4500008004100000022001400041245009200055210006900147300001400216490000600230100001900236856004800255 2011 eng d a1664-236800aBoutroux curves with external field: equilibrium measures without a variational problem0 aBoutroux curves with external field equilibrium measures without a167–2110 v11 aBertola, Marco uhttp://dx.doi.org/10.1007/s13324-011-0012-300554nas a2200121 4500008004100000245011500041210006900156300000900225490002900234100001900263700002000282856013000302 2011 eng d00aThe Transition between the Gap Probabilities from the Pearcey to the Airy Process–a Riemann-Hilbert Approach0 aTransition between the Gap Probabilities from the Pearcey to the a1-500 vdoi: 10.1093/imrn/rnr0661 aBertola, Marco1 aCafasso, Mattia uhttps://math.sissa.it/publication/transition-between-gap-probabilities-pearcey-airy-process%E2%80%93-riemann-hilbert-approach00422nas a2200145 4500008004100000022001400041245003600055210003600091300001400127490000800141100001900149700001700168700002000185856007100205 2010 eng d a0021-904500aCauchy biorthogonal polynomials0 aCauchy biorthogonal polynomials a832–8670 v1621 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2009.09.00800433nas a2200121 4500008004100000022001400041245007500055210006900130300001400199490000800213100001900221856007100240 2010 eng d a0010-361600aThe dependence on the monodromy data of the isomonodromic tau function0 adependence on the monodromy data of the isomonodromic tau functi a539–5790 v2941 aBertola, Marco uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-009-0961-700439nas a2200133 4500008004100000022001400041245006200055210006100117300001400178490000700192100001900199700001600218856007100234 2010 eng d a0176-427600aFirst colonization of a hard-edge in random matrix theory0 aFirst colonization of a hardedge in random matrix theory a231–2570 v311 aBertola, Marco1 aLee, S., Y. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-009-9052-400513nas a2200121 4500008004100000022001400041245014500055210006900200300001600269100001900285700002200304856006500326 2010 eng d a1073-792800aUniversality in the profile of the semiclassical limit solutions to the focusing nonlinear Schrödinger equation at the first breaking curve0 aUniversality in the profile of the semiclassical limit solutions a2119–21671 aBertola, Marco1 aTovbis, Alexander uhttp://0-dx.doi.org.mercury.concordia.ca/10.1093/imrn/rnp19600386nas a2200133 4500008004100000245003400041210003000075300001500105490000800120100001900128700001600147700001900163856007000182 2009 eng d00aThe Cauchy two–matrix model0 aCauchy two–matrix model a983–10140 v2871 aBertola, Marco1 aGekhtman, M1 aSzmigielski, J uhttps://math.sissa.it/publication/cauchy-two%E2%80%93matrix-model00574nas a2200133 4500008004100000022001400041245013700055210006900192300001400261490000800275100001900283700001500302856012300317 2009 eng d a0001-870800aCommuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights0 aCommuting difference operators spinor bundles and the asymptotic a154–2180 v2201 aBertola, Marco1 aMo, M., Y. uhttps://math.sissa.it/publication/commuting-difference-operators-spinor-bundles-and-asymptotics-orthogonal-polynomials00501nas a2200145 4500008004100000022001400041245007700055210006900132300001500201490000700216100001900223700001700242700002000259856007600279 2009 eng d a1751-811300aCubic string boundary value problems and Cauchy biorthogonal polynomials0 aCubic string boundary value problems and Cauchy biorthogonal pol a454006, 130 v421 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/45/45400600454nas a2200133 4500008004100000022001400041245006900055210006900124300001400193490000700207100001900214700001600233856007100249 2009 eng d a0176-427600aFirst colonization of a spectral outpost in random matrix theory0 aFirst colonization of a spectral outpost in random matrix theory a225–2630 v301 aBertola, Marco1 aLee, S., Y. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-008-9026-y00443nas a2200145 4500008004100000022001400041245004700055210004700102300001500149490000700164100001900171700001600190700001500206856007600221 2009 eng d a1751-811300aMesoscopic colonization in a spectral band0 aMesoscopic colonization in a spectral band a415204, 170 v421 aBertola, Marco1 aLee, S., Y.1 aMo, M., Y. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/41/41520400385nas a2200109 4500008004100000245005500041210005500096300001200151490000700163100001900170856008600189 2009 eng d00aMoment determinants as isomonodromic tau functions0 aMoment determinants as isomonodromic tau functions a29–500 v221 aBertola, Marco uhttps://math.sissa.it/publication/moment-determinants-isomonodromic-tau-functions00462nas a2200133 4500008004100000022001400041245008300055210007000138300001500208490000700223100001900230700001600249856006300265 2009 eng d a0022-248800aThe partition function of the two-matrix model as an isomonodromic τ function0 apartition function of the twomatrix model as an isomonodromic τ a013529, 170 v501 aBertola, Marco1 aMarchal, O. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1063/1.305486500456nas a2200133 4500008004100000022001400041245006800055210006800123300001400191490000800205100001900213700001900232856007100251 2009 eng d a0021-904500aRegularity of a vector potential problem and its spectral curve0 aRegularity of a vector potential problem and its spectral curve a353–3700 v1611 aBalogh, Ferenc1 aBertola, Marco uhttp://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2008.10.01000416nas a2200133 4500008004100000022001400041245005800055210005700113300001500170490000700185100001900192700001800211856005300229 2009 eng d a1751-811300aTopological expansion for the Cauchy two-matrix model0 aTopological expansion for the Cauchy twomatrix model a335201, 280 v421 aBertola, Marco1 aFerrer, Prats uhttp://dx.doi.org/10.1088/1751-8113/42/33/33520100430nas a2200121 4500008004100000022001400041245005200055210005100107300002300158100001900181700002500200856008300225 2008 eng d a1073-792800aHarish-Chandra integrals as nilpotent integrals0 aHarishChandra integrals as nilpotent integrals aArt. ID rnn062, 151 aBertola, Marco1 aFerrer, Aleix, Prats uhttps://math.sissa.it/publication/harish-chandra-integrals-nilpotent-integrals00550nas a2200133 4500008004100000022001400041245011300055210007000168300001400238490000700252100001900259700001700278856012100295 2007 eng d a0176-427600aBiorthogonal Laurent polynomials, Töplitz determinants, minimal Toda orbits and isomonodromic tau functions0 aBiorthogonal Laurent polynomials Töplitz determinants minimal To a383–4300 v261 aBertola, Marco1 aGekhtman, M. uhttps://math.sissa.it/publication/biorthogonal-laurent-polynomials-t%C3%B6plitz-determinants-minimal-toda-orbits-and00474nas a2200121 4500008004100000022001400041245008100055210006900136300001400205490000800219100001900227856010600246 2007 eng d a0021-904500aBiorthogonal polynomials for two-matrix models with semiclassical potentials0 aBiorthogonal polynomials for twomatrix models with semiclassical a162–2120 v1441 aBertola, Marco uhttps://math.sissa.it/publication/biorthogonal-polynomials-two-matrix-models-semiclassical-potentials00499nas a2200121 4500008004100000022001400041245008200055210006900137300002300206100001900229700001700248856011200265 2007 eng d a1073-792800aEffective inverse spectral problem for rational Lax matrices and applications0 aEffective inverse spectral problem for rational Lax matrices and aArt. ID rnm103, 391 aBertola, Marco1 aGekhtman, M. uhttps://math.sissa.it/publication/effective-inverse-spectral-problem-rational-lax-matrices-and-applications00518nas a2200145 4500008004100000245006600041210006500107260002300172300001200195490000800207100001900215700002400234700001900258856009500277 2007 eng d00aMassless scalar field in a two-dimensional de Sitter universe0 aMassless scalar field in a twodimensional de Sitter universe aBaselbBirkhäuser a27–380 v2511 aBertola, Marco1 aCorbetta, Francesco1 aMoschella, Ugo uhttps://math.sissa.it/publication/massless-scalar-field-two-dimensional-de-sitter-universe00475nas a2200133 4500008004100000022001400041245007300055210006800128300001200196490000600208100001900214700001500233856009300248 2006 eng d a1385-017200aThe PDEs of biorthogonal polynomials arising in the two-matrix model0 aPDEs of biorthogonal polynomials arising in the twomatrix model a23–520 v91 aBertola, Marco1 aEynard, B. uhttps://math.sissa.it/publication/pdes-biorthogonal-polynomials-arising-two-matrix-model00550nas a2200145 4500008004100000022001400041245008800055210006900143300001400212490000800226100001900234700001500253700001500268856012100283 2006 eng d a0010-361600aSemiclassical orthogonal polynomials, matrix models and isomonodromic tau functions0 aSemiclassical orthogonal polynomials matrix models and isomonodr a401–4370 v2631 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttps://math.sissa.it/publication/semiclassical-orthogonal-polynomials-matrix-models-and-isomonodromic-tau-functions00481nas a2200121 4500008004100000022001400041245008200055210006900137300001600206490000700222100001900229856011100248 2006 eng d a0305-447000aTwo-matrix model with semiclassical potentials and extended Whitham hierarchy0 aTwomatrix model with semiclassical potentials and extended Whith a8823–88550 v391 aBertola, Marco uhttps://math.sissa.it/publication/two-matrix-model-semiclassical-potentials-and-extended-whitham-hierarchy00445nas a2200121 4500008004100000022001400041245006300055210006300118300001400181100001900195700001500214856009400229 2005 eng d a1687-301700aIsomonodromic deformation of resonant rational connections0 aIsomonodromic deformation of resonant rational connections a565–6351 aBertola, Marco1 aMo, M., Y. uhttps://math.sissa.it/publication/isomonodromic-deformation-resonant-rational-connections00479nas a2200121 4500008004100000022001400041245008000055210006900135300001200204490000800216100001900224856011400243 2003 eng d a0021-904500aBilinear semiclassical moment functionals and their integral representation0 aBilinear semiclassical moment functionals and their integral rep a71–990 v1211 aBertola, Marco uhttps://math.sissa.it/publication/bilinear-semiclassical-moment-functionals-and-their-integral-representation00592nas a2200145 4500008004100000022001400041245012600055210006900181300001400250490000800264100001900272700001500291700001500306856012500321 2003 eng d a0010-361600aDifferential systems for biorthogonal polynomials appearing in 2-matrix models and the associated Riemann-Hilbert problem0 aDifferential systems for biorthogonal polynomials appearing in 2 a193–2400 v2431 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttps://math.sissa.it/publication/differential-systems-biorthogonal-polynomials-appearing-2-matrix-models-and-associated00491nas a2200145 4500008004100000022001400041245006800055210006300123300001200186490000800198100001900206700001500225700001800240856008700258 2003 eng d a0564-616200aThe duality of spectral curves that arises in two-matrix models0 aduality of spectral curves that arises in twomatrix models a32–450 v1341 aBertola, Marco1 aEynard, B.1 aKharnad, Dzh. uhttps://math.sissa.it/publication/duality-spectral-curves-arises-two-matrix-models00418nas a2200121 4500008004100000022001400041245005900055210005600114300001400170490000800184100001900192856008500211 2003 eng d a0550-321300aFree energy of the two-matrix model/dToda tau-function0 aFree energy of the twomatrix modeldToda taufunction a435–4610 v6691 aBertola, Marco uhttps://math.sissa.it/publication/free-energy-two-matrix-modeldtoda-tau-function00440nas a2200133 4500008004100000022001400041245005600055210005500111300001600166490000700182100001900189700001500208856008300223 2003 eng d a0305-447000aMixed correlation functions of the two-matrix model0 aMixed correlation functions of the twomatrix model a7733–77500 v361 aBertola, Marco1 aEynard, B. uhttps://math.sissa.it/publication/mixed-correlation-functions-two-matrix-model00520nas a2200145 4500008004100000022001400041245007400055210006900129300001600198490000700214100001900221700001500240700001500255856010400270 2003 eng d a0305-447000aPartition functions for matrix models and isomonodromic tau functions0 aPartition functions for matrix models and isomonodromic tau func a3067–30830 v361 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttps://math.sissa.it/publication/partition-functions-matrix-models-and-isomonodromic-tau-functions00428nas a2200109 4500008004100000022001400041245006300055210006200118300002900180100001900209856009000228 2003 eng d a1126-670800aSecond and third order observables of the two-matrix model0 aSecond and third order observables of the twomatrix model a062, 30 pp. (electronic)1 aBertola, Marco uhttps://math.sissa.it/publication/second-and-third-order-observables-two-matrix-model00457nas a2200133 4500008004100000022001400041245006600055210005700121300001600178490000700194100002100201700001900222856008200241 2002 eng d a0022-248800aCoherent state realizations of $\rm su(n+1)$ on the $n$-torus0 aCoherent state realizations of rm sun1 on the ntorus a3425–34440 v431 ade Guise, Hubert1 aBertola, Marco uhttps://math.sissa.it/publication/coherent-state-realizations-rm-sun1-n-torus00488nas a2200145 4500008004100000022001400041245006200055210006000117300001300177490000800190100001900198700001500217700001500232856009500247 2002 eng d a0010-361600aDuality, biorthogonal polynomials and multi-matrix models0 aDuality biorthogonal polynomials and multimatrix models a73–1200 v2291 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttps://math.sissa.it/publication/duality-biorthogonal-polynomials-and-multi-matrix-models00436nas a2200121 4500008004100000245005500041210005400096260003700150300001300187490000700200100001900207856008800226 2002 eng d00aJacobi groups, Jacobi forms and their applications0 aJacobi groups Jacobi forms and their applications aProvidence, RIbAmer. Math. Soc. a99–1110 v311 aBertola, Marco uhttps://math.sissa.it/publication/jacobi-groups-jacobi-forms-and-their-applications00409nas a2200133 4500008004100000022001400041245004300055210004300098300001400141490000700155100001900162700001700181856007700198 2001 eng d a1120-718300aLie triple systems and warped products0 aLie triple systems and warped products a275–2930 v211 aBertola, Marco1 aGouthier, D. uhttps://math.sissa.it/publication/lie-triple-systems-and-warped-products00440nas a2200133 4500008004100000022001400041245005400055210005400109300001200163490000700175100001900182700002200201856008300223 2001 eng d a0100-356900aWarped products with special Riemannian curvature0 aWarped products with special Riemannian curvature a45–620 v321 aBertola, Marco1 aGouthier, Daniele uhttps://math.sissa.it/publication/warped-products-special-riemannian-curvature00501nas a2200169 4500008004100000022001400041245004100055210004100096300001400137490000800151100001900159700001800178700002100196700001900217700002300236856007200259 2000 eng d a0550-321300aDecomposing quantum fields on branes0 aDecomposing quantum fields on branes a575–6030 v5811 aBertola, Marco1 aBros, Jacques1 aGorini, Vittorio1 aMoschella, Ugo1 aSchaeffer, Richard uhttps://math.sissa.it/publication/decomposing-quantum-fields-branes00445nas a2200121 4500008004100000022001400041245006800055210006700123300001200190490000700202100001900209856009500228 2000 eng d a0926-224500aFrobenius manifold structure on orbit space of Jacobi groups. I0 aFrobenius manifold structure on orbit space of Jacobi groups I a19–410 v131 aBertola, Marco uhttps://math.sissa.it/publication/frobenius-manifold-structure-orbit-space-jacobi-groups-i00450nas a2200121 4500008004100000022001400041245006900055210006800124300001400192490000700206100001900213856009600232 2000 eng d a0926-224500aFrobenius manifold structure on orbit space of Jacobi groups. II0 aFrobenius manifold structure on orbit space of Jacobi groups II a213–2330 v131 aBertola, Marco uhttps://math.sissa.it/publication/frobenius-manifold-structure-orbit-space-jacobi-groups-ii00608nas a2200157 4500008004100000022001400041245010500055210006900160300001400229490000800243100001900251700001800270700001900288700002300307856012000330 2000 eng d a0550-321300aA general construction of conformal field theories from scalar anti-de Sitter quantum field theories0 ageneral construction of conformal field theories from scalar ant a619–6440 v5871 aBertola, Marco1 aBros, Jacques1 aMoschella, Ugo1 aSchaeffer, Richard uhttps://math.sissa.it/publication/general-construction-conformal-field-theories-scalar-anti-de-sitter-quantum-field00564nas a2200157 4500008004100000022001400041245007200055210006900127300001400196490000800210100001900218700002100237700001900258700002300277856010600300 1999 eng d a0370-269300aCorrespondence between Minkowski and de Sitter quantum field theory0 aCorrespondence between Minkowski and de Sitter quantum field the a249–2530 v4621 aBertola, Marco1 aGorini, Vittorio1 aMoschella, Ugo1 aSchaeffer, Richard uhttps://math.sissa.it/publication/correspondence-between-minkowski-and-de-sitter-quantum-field-theory00520nas a2200157 4500008004100000022001400041245005900055210005900114300001400173490000600187100002300193700001900216700001900235700002100254856008700275 1998 eng d a0202-289300aGeneration of primordial fluctuations in curved spaces0 aGeneration of primordial fluctuations in curved spaces a121–1270 v41 aSchaeffer, Richard1 aMoschella, Ugo1 aBertola, Marco1 aGorini, Vittorio uhttps://math.sissa.it/publication/generation-primordial-fluctuations-curved-spaces