TY - JOUR T1 - Discriminant circle bundles over local models of Strebel graphs and Boutroux curves JF - Teoret. Mat. Fiz. Y1 - 2018 A1 - Marco Bertola A1 - Korotkin, D. A. VL - 197 UR - https://doi.org/10.4213/tmf9513 ER - TY - JOUR T1 - Noncommutative Painlevé Equations and Systems of Calogero Type JF - Comm. Math. Phys Y1 - 2018 A1 - Marco Bertola A1 - Mattia Cafasso A1 - V. Rubtsov ER - TY - JOUR T1 - Painlevé IV Critical Asymptotics for Orthogonal Polynomials in the Complex Plane JF - Symmetry, Integrability and Geometry. Methods and Applications Y1 - 2018 A1 - Marco Bertola A1 - José Gustavo Elias Rebelo A1 - Tamara Grava AB -

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.

PB - National Academy of Sciences of Ukraine VL - 14 ER - TY - JOUR T1 - The Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes' phenomenon JF - Comm. Math. Phys Y1 - 2017 A1 - Marco Bertola A1 - Mattia Cafasso VL - DOI 10.1007/s00220-017-2856-3 UR - http://arxiv.org/abs/1603.06420 ER - TY - JOUR T1 - The Malgrange form and Fredholm determinants JF - SIGMA Symmetry Integrability Geom. Methods Appl. Y1 - 2017 A1 - Marco Bertola VL - 13 UR - http://dx.doi.org/10.3842/SIGMA.2017.046 ER - TY - JOUR T1 - Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation JF - Comm. Math. Phys. Y1 - 2017 A1 - Marco Bertola A1 - Alexander Tovbis VL - 354 UR - http://dx.doi.org/10.1007/s00220-017-2895-9 ER - TY - JOUR T1 - Symplectic geometry of the moduli space of projective structures in homological coordinates JF - Inventiones Mathematicae Y1 - 2017 A1 - Marco Bertola A1 - Dmitry Korotkin A1 - Chaya Norton UR - https://arxiv.org/abs/1506.07918 ER - TY - JOUR T1 - Universality of the matrix Airy and Bessel functions at spectral edges of unitary ensembles JF - Random Matrices Theory Appl. Y1 - 2017 A1 - Marco Bertola A1 - Mattia Cafasso VL - 6 UR - http://dx.doi.org/10.1142/S2010326317500101 ER - TY - JOUR T1 - Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation JF - Phys. Rev. Lett. Y1 - 2017 A1 - Tikan, Alexey A1 - Billet, Cyril A1 - Gennady El A1 - Alexander Tovbis A1 - Marco Bertola A1 - Sylvestre, Thibaut A1 - Gustave, Francois A1 - Randoux, Stephane A1 - Genty, Goëry A1 - Suret, Pierre A1 - Dudley, John M. PB - American Physical Society VL - 119 UR - https://link.aps.org/doi/10.1103/PhysRevLett.119.033901 ER - TY - JOUR T1 - On asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight JF - SIGMA Symmetry Integrability Geom. Methods Appl. Y1 - 2016 A1 - Marco Bertola A1 - Alexander Tovbis VL - 12 UR - http://dx.doi.org/10.3842/SIGMA.2016.118 ER - TY - JOUR T1 - Correlation functions of the KdV hierarchy and applications to intersection numbers over $\overline\CalM_g,n$ JF - Phys. D Y1 - 2016 A1 - Marco Bertola A1 - Boris Dubrovin A1 - Di Yang VL - 327 UR - http://dx.doi.org/10.1016/j.physd.2016.04.008 ER - TY - JOUR T1 - CORRIGENDUM: The dependence on the monodromy data of the isomonodromic tau function Y1 - 2016 A1 - Marco Bertola UR - http://arxiv.org/abs/1601.04790 ER - TY - JOUR T1 - Hankel determinant approach to generalized Vorob'ev-Yablonski polynomials and their roots JF - Constr. Approx. Y1 - 2016 A1 - Ferenc Balogh A1 - Marco Bertola A1 - Thomas Bothner VL - 44 UR - http://dx.doi.org/10.1007/s00365-016-9328-4 ER - TY - JOUR T1 - Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation JF - Proc. A. Y1 - 2016 A1 - Marco Bertola A1 - Gennady El A1 - Alexander Tovbis VL - 472 UR - http://dx.doi.org/10.1098/rspa.2016.0340 ER - TY - JOUR T1 - Simple Lie Algebras and Topological ODEs JF - Int. Math. Res. Not. Y1 - 2016 A1 - Marco Bertola A1 - Boris Dubrovin A1 - Di Yang VL - 2016 ER - TY - JOUR T1 - On Sobolev instability of the interior problem of tomography JF - Journal of Mathematical Analysis and Applications Y1 - 2016 A1 - Marco Bertola A1 - Alexander Katsevich A1 - Alexander Tovbis ER - TY - JOUR T1 - Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation JF - Constr. Approx. Y1 - 2015 A1 - Marco Bertola A1 - Alexander Tovbis VL - 41 UR - http://dx.doi.org/10.1007/s00365-015-9288-0 ER - TY - JOUR T1 - A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems JF - J. Math. Phys. Y1 - 2015 A1 - Marco Bertola A1 - Giavedoni, Pietro VL - 56 UR - http://dx.doi.org/10.1063/1.4922362 ER - TY - JOUR T1 - Meromorphic differentials with imaginary periods on degenerating hyperelliptic curves JF - Anal. Math. Phys. Y1 - 2015 A1 - Marco Bertola A1 - Alexander Tovbis VL - 5 UR - http://dx.doi.org/10.1007/s13324-014-0088-7 ER - TY - JOUR T1 - The partition function of the extended $r$-reduced Kadomtsev-Petviashvili hierarchy JF - J. Phys. A Y1 - 2015 A1 - Marco Bertola A1 - Di Yang VL - 48 UR - http://dx.doi.org/10.1088/1751-8113/48/19/195205 ER - TY - JOUR T1 - Strong asymptotics of the orthogonal polynomials with respect to a measure supported on the plane JF - Comm. Pure Appl. Math. Y1 - 2015 A1 - Ferenc Balogh A1 - Marco Bertola A1 - Lee, Seung-Yeop A1 - Kenneth McLaughlin VL - 68 UR - http://dx.doi.org/10.1002/cpa.21541 ER - TY - JOUR T1 - Universality Conjecture and Results for a Model of Several Coupled Positive-Definite Matrices JF - Commun. Math. Phys. Y1 - 2015 A1 - Marco Bertola A1 - Thomas Bothner VL - 337 UR - http://link.springer.com/article/10.1007/s00220-015-2327-7 ER - TY - JOUR T1 - Cauchy-Laguerre two-matrix model and the Meijer-G random point field JF - Comm. Math. Phys. Y1 - 2014 A1 - Marco Bertola A1 - Gekhtman, M. A1 - Szmigielski, J. VL - 326 UR - http://dx.doi.org/10.1007/s00220-013-1833-8 ER - TY - JOUR T1 - Darboux Transformations and Random Point Processes JF - IMRN Y1 - 2014 A1 - Marco Bertola A1 - Mattia Cafasso VL - rnu122 ER - TY - JOUR T1 - Singular Value Decomposition of a Finite Hilbert Transform Defined on Several Intervals and the Interior Problem of Tomography: The Riemann-Hilbert Problem Approach JF - Comm. Pure Appl. Math. Y1 - 2014 A1 - Marco Bertola A1 - Alexander Katsevich A1 - Alexander Tovbis ER - TY - JOUR T1 - Zeros of Large Degree Vorob'ev-Yablonski Polynomials via a Hankel Determinant Identity JF - International Mathematics Research Notices Y1 - 2014 A1 - Marco Bertola A1 - Thomas Bothner VL - rnu239 ER - TY - JOUR T1 - The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation JF - Random Matrices: Theory and Applications Y1 - 2013 A1 - Marco Bertola A1 - Mattia Cafasso VL - 02 UR - http://www.worldscientific.com/doi/abs/10.1142/S2010326313500032 ER - TY - JOUR T1 - Inversion formulae for the $\romancosh$-weighted Hilbert transform JF - Proc. Amer. Math. Soc. Y1 - 2013 A1 - Marco Bertola A1 - Katsevich, A. A1 - Alexander Tovbis VL - 141 UR - http://dx.doi.org/10.1090/S0002-9939-2013-11642-4 ER - TY - JOUR T1 - Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes JF - J. Stat. Phys. Y1 - 2013 A1 - Marco Bertola A1 - Buckingham, R. A1 - Lee, S. Y. A1 - Pierce, V. VL - 153 UR - http://dx.doi.org/10.1007/s10955-013-0845-2 ER - TY - JOUR T1 - Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model JF - J. Math. Phys. Y1 - 2013 A1 - Marco Bertola A1 - Gekhtman, M. A1 - Szmigielski, J. VL - 54 ER - TY - JOUR T1 - Universality for the focusing nonlinear Schrödinger equation at the gradient catastrophe point: rational breathers and poles of the \it Tritronquée solution to Painlevé I JF - Comm. Pure Appl. Math. Y1 - 2013 A1 - Marco Bertola A1 - Alexander Tovbis VL - 66 UR - http://dx.doi.org/10.1002/cpa.21445 ER - TY - JOUR T1 - Fredholm determinants and pole-free solutions to the noncommutative Painlevé II equation JF - Comm. Math. Phys. Y1 - 2012 A1 - Marco Bertola A1 - Mattia Cafasso VL - 309 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-011-1383-x ER - TY - JOUR T1 - On the location of poles for the Ablowitz-Segur family of solutions to the second Painlevé equation JF - Nonlinearity Y1 - 2012 A1 - Marco Bertola VL - 25 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1088/0951-7715/25/4/1179 ER - TY - JOUR T1 - Riemann–Hilbert approach to multi-time processes: The Airy and the Pearcey cases JF - Physica D: Nonlinear Phenomena Y1 - 2012 A1 - Marco Bertola A1 - Mattia Cafasso KW - Integrable kernels VL - 241 UR - http://www.sciencedirect.com/science/article/pii/S0167278912000115 N1 - Integrable Systems in Pure and Applied Mathematics ER - TY - JOUR T1 - Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes JF - J. Stat. Phys. Y1 - 2012 A1 - Marco Bertola A1 - Buckingham, R. A1 - Lee, S. Y. A1 - Pierce, V. VL - 146 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s10955-011-0409-2 ER - TY - JOUR T1 - Boutroux curves with external field: equilibrium measures without a variational problem JF - Anal. Math. Phys. Y1 - 2011 A1 - Marco Bertola VL - 1 UR - http://dx.doi.org/10.1007/s13324-011-0012-3 ER - TY - JOUR T1 - The Transition between the Gap Probabilities from the Pearcey to the Airy Process–a Riemann-Hilbert Approach JF - International Mathematics Research Notices Y1 - 2011 A1 - Marco Bertola A1 - Mattia Cafasso VL - doi: 10.1093/imrn/rnr066 ER - TY - JOUR T1 - Cauchy biorthogonal polynomials JF - J. Approx. Theory Y1 - 2010 A1 - Marco Bertola A1 - Gekhtman, M. A1 - Szmigielski, J. VL - 162 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2009.09.008 ER - TY - JOUR T1 - The dependence on the monodromy data of the isomonodromic tau function JF - Comm. Math. Phys. Y1 - 2010 A1 - Marco Bertola VL - 294 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-009-0961-7 ER - TY - JOUR T1 - First colonization of a hard-edge in random matrix theory JF - Constr. Approx. Y1 - 2010 A1 - Marco Bertola A1 - Lee, S. Y. VL - 31 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-009-9052-4 ER - TY - JOUR T1 - Universality in the profile of the semiclassical limit solutions to the focusing nonlinear Schrödinger equation at the first breaking curve JF - Int. Math. Res. Not. IMRN Y1 - 2010 A1 - Marco Bertola A1 - Alexander Tovbis UR - http://0-dx.doi.org.mercury.concordia.ca/10.1093/imrn/rnp196 ER - TY - JOUR T1 - The Cauchy two–matrix model JF - Comm. Math. Phys. Y1 - 2009 A1 - Marco Bertola A1 - M Gekhtman A1 - J Szmigielski VL - 287 ER - TY - JOUR T1 - Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights JF - Adv. Math. Y1 - 2009 A1 - Marco Bertola A1 - Mo, M. Y. VL - 220 ER - TY - JOUR T1 - Cubic string boundary value problems and Cauchy biorthogonal polynomials JF - J. Phys. A Y1 - 2009 A1 - Marco Bertola A1 - Gekhtman, M. A1 - Szmigielski, J. VL - 42 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/45/454006 ER - TY - JOUR T1 - First colonization of a spectral outpost in random matrix theory JF - Constr. Approx. Y1 - 2009 A1 - Marco Bertola A1 - Lee, S. Y. VL - 30 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-008-9026-y ER - TY - JOUR T1 - Mesoscopic colonization in a spectral band JF - J. Phys. A Y1 - 2009 A1 - Marco Bertola A1 - Lee, S. Y. A1 - Mo, M. Y. VL - 42 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/41/415204 ER - TY - JOUR T1 - Moment determinants as isomonodromic tau functions JF - Nonlinearity Y1 - 2009 A1 - Marco Bertola VL - 22 ER - TY - JOUR T1 - The partition function of the two-matrix model as an isomonodromic τ function JF - J. Math. Phys. Y1 - 2009 A1 - Marco Bertola A1 - Marchal, O. VL - 50 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1063/1.3054865 ER - TY - JOUR T1 - Regularity of a vector potential problem and its spectral curve JF - J. Approx. Theory Y1 - 2009 A1 - Ferenc Balogh A1 - Marco Bertola VL - 161 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2008.10.010 ER - TY - JOUR T1 - Topological expansion for the Cauchy two-matrix model JF - J. Phys. A Y1 - 2009 A1 - Marco Bertola A1 - Ferrer, A. Prats VL - 42 UR - http://dx.doi.org/10.1088/1751-8113/42/33/335201 ER - TY - JOUR T1 - Harish-Chandra integrals as nilpotent integrals JF - Int. Math. Res. Not. IMRN Y1 - 2008 A1 - Marco Bertola A1 - Ferrer, Aleix Prats ER - TY - JOUR T1 - Biorthogonal Laurent polynomials, Töplitz determinants, minimal Toda orbits and isomonodromic tau functions JF - Constr. Approx. Y1 - 2007 A1 - Marco Bertola A1 - Gekhtman, M. VL - 26 ER - TY - JOUR T1 - Biorthogonal polynomials for two-matrix models with semiclassical potentials JF - J. Approx. Theory Y1 - 2007 A1 - Marco Bertola VL - 144 ER - TY - JOUR T1 - Effective inverse spectral problem for rational Lax matrices and applications JF - Int. Math. Res. Not. IMRN Y1 - 2007 A1 - Marco Bertola A1 - Gekhtman, M. ER - TY - CHAP T1 - Massless scalar field in a two-dimensional de Sitter universe T2 - Rigorous quantum field theory Y1 - 2007 A1 - Marco Bertola A1 - Corbetta, Francesco A1 - Moschella, Ugo JF - Rigorous quantum field theory T3 - Progr. Math. PB - Birkhäuser CY - Basel VL - 251 ER - TY - JOUR T1 - The PDEs of biorthogonal polynomials arising in the two-matrix model JF - Math. Phys. Anal. Geom. Y1 - 2006 A1 - Marco Bertola A1 - B. Eynard VL - 9 ER - TY - JOUR T1 - Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions JF - Comm. Math. Phys. Y1 - 2006 A1 - Marco Bertola A1 - B. Eynard A1 - Harnad, J. VL - 263 ER - TY - JOUR T1 - Two-matrix model with semiclassical potentials and extended Whitham hierarchy JF - J. Phys. A Y1 - 2006 A1 - Marco Bertola VL - 39 ER - TY - JOUR T1 - Isomonodromic deformation of resonant rational connections JF - IMRP Int. Math. Res. Pap. Y1 - 2005 A1 - Marco Bertola A1 - Mo, M. Y. ER - TY - JOUR T1 - Bilinear semiclassical moment functionals and their integral representation JF - J. Approx. Theory Y1 - 2003 A1 - Marco Bertola VL - 121 ER - TY - JOUR T1 - Differential systems for biorthogonal polynomials appearing in 2-matrix models and the associated Riemann-Hilbert problem JF - Comm. Math. Phys. Y1 - 2003 A1 - Marco Bertola A1 - B. Eynard A1 - Harnad, J. VL - 243 ER - TY - JOUR T1 - The duality of spectral curves that arises in two-matrix models JF - Teoret. Mat. Fiz. Y1 - 2003 A1 - Marco Bertola A1 - B. Eynard A1 - Kharnad, Dzh. VL - 134 ER - TY - JOUR T1 - Free energy of the two-matrix model/dToda tau-function JF - Nuclear Phys. B Y1 - 2003 A1 - Marco Bertola VL - 669 ER - TY - JOUR T1 - Mixed correlation functions of the two-matrix model JF - J. Phys. A Y1 - 2003 A1 - Marco Bertola A1 - B. Eynard VL - 36 ER - TY - JOUR T1 - Partition functions for matrix models and isomonodromic tau functions JF - J. Phys. A Y1 - 2003 A1 - Marco Bertola A1 - B. Eynard A1 - Harnad, J. VL - 36 N1 - Random matrix theory ER - TY - JOUR T1 - Second and third order observables of the two-matrix model JF - J. High Energy Phys. Y1 - 2003 A1 - Marco Bertola ER - TY - JOUR T1 - Coherent state realizations of $\rm su(n+1)$ on the $n$-torus JF - J. Math. Phys. Y1 - 2002 A1 - de Guise, Hubert A1 - Marco Bertola VL - 43 ER - TY - JOUR T1 - Duality, biorthogonal polynomials and multi-matrix models JF - Comm. Math. Phys. Y1 - 2002 A1 - Marco Bertola A1 - B. Eynard A1 - Harnad, J. VL - 229 ER - TY - CHAP T1 - Jacobi groups, Jacobi forms and their applications T2 - Isomonodromic deformations and applications in physics (Montréal, QC, 2000) Y1 - 2002 A1 - Marco Bertola JF - Isomonodromic deformations and applications in physics (Montréal, QC, 2000) T3 - CRM Proc. Lecture Notes PB - Amer. Math. Soc. CY - Providence, RI VL - 31 ER - TY - JOUR T1 - Lie triple systems and warped products JF - Rend. Mat. Appl. (7) Y1 - 2001 A1 - Marco Bertola A1 - Gouthier, D. VL - 21 ER - TY - JOUR T1 - Warped products with special Riemannian curvature JF - Bol. Soc. Brasil. Mat. (N.S.) Y1 - 2001 A1 - Marco Bertola A1 - Gouthier, Daniele VL - 32 ER - TY - JOUR T1 - Decomposing quantum fields on branes JF - Nuclear Phys. B Y1 - 2000 A1 - Marco Bertola A1 - Bros, Jacques A1 - Gorini, Vittorio A1 - Moschella, Ugo A1 - Schaeffer, Richard VL - 581 ER - TY - JOUR T1 - Frobenius manifold structure on orbit space of Jacobi groups. I JF - Differential Geom. Appl. Y1 - 2000 A1 - Marco Bertola VL - 13 ER - TY - JOUR T1 - Frobenius manifold structure on orbit space of Jacobi groups. II JF - Differential Geom. Appl. Y1 - 2000 A1 - Marco Bertola VL - 13 ER - TY - JOUR T1 - A general construction of conformal field theories from scalar anti-de Sitter quantum field theories JF - Nuclear Phys. B Y1 - 2000 A1 - Marco Bertola A1 - Bros, Jacques A1 - Moschella, Ugo A1 - Schaeffer, Richard VL - 587 ER - TY - JOUR T1 - Correspondence between Minkowski and de Sitter quantum field theory JF - Phys. Lett. B Y1 - 1999 A1 - Marco Bertola A1 - Gorini, Vittorio A1 - Moschella, Ugo A1 - Schaeffer, Richard VL - 462 ER - TY - JOUR T1 - Generation of primordial fluctuations in curved spaces JF - Gravit. Cosmol. Y1 - 1998 A1 - Schaeffer, Richard A1 - Moschella, Ugo A1 - Marco Bertola A1 - Gorini, Vittorio VL - 4 ER -