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 - 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 - Finite dimensional Kadomtsev-Petviashvili τ-functions. I. Finite Grassmannians Y1 - 2014 A1 - Ferenc Balogh A1 - Tiago Fonseca A1 - John P. Harnad AB - We study τ-functions of the Kadomtsev-Petviashvili hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal, and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Plücker coordinates appearing as coefficients in the Schur function expansion of the τ-function. PB - American Institute of Physics Inc. UR - http://urania.sissa.it/xmlui/handle/1963/34952 U1 - 35153 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Weighted quantile correlation test for the logistic family Y1 - 2014 A1 - Ferenc Balogh A1 - Éva Krauczi AB - We summarize the results of investigating the asymptotic behavior of the weighted quantile correlation tests for the location-scale family associated to the logistic distribution. Explicit representations of the limiting distribution are given in terms of integrals of weighted Brownian bridges or alternatively as infinite series of independent Gaussian random variables. The power of this test and the test for the location logistic family against some alternatives are demonstrated by numerical simulations. PB - University of Szeged UR - http://urania.sissa.it/xmlui/handle/1963/35025 U1 - 35261 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Equilibrium measures for a class of potentials with discrete rotational symmetries Y1 - 2013 A1 - Ferenc Balogh A1 - Dario Merzi AB - In this note the logarithmic energy problem with external potential $|z|^{2n}+tz^d+\bar{t}\bar{z}^d$ is considered in the complex plane, where $n$ and $d$ are positive integers satisfying $d\leq 2n$. Exploiting the discrete rotational invariance of the potential, a simple symmetry reduction procedure is used to calculate the equilibrium measure for all admissible values of $n,d$ and $t$. It is shown that, for fixed $n$ and $d$, there is a critical value $|t|=t_{cr}$ such that the support of the equilibrium measure is simply connected for $|t|t_{cr}$. PB - SISSA UR - http://hdl.handle.net/1963/7230 N1 - 23 pages, 3 figures U1 - 7270 U2 - Mathematics U4 - 1 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 -