The Hermitian two matrix model with an even quartic potential

DOI10.1090/S0065-9266-2011-00639-8zbMath1247.15032arXiv1010.4282MaRDI QIDQ2882489

Maurice Duits, Man Yue Mo, Arno B. J. Kuijlaars

Publication date: 6 May 2012

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.4282

zbMATH Keywords

Riemann-Hilbert problemeigenvalue distributionHamiltonian matricesquartic potentialbiorthogonal polynomialsvector equilibrium problemsteepest descent methodsaddle point equationHermitian two matrix model

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Compact Riemann surfaces and uniformization (30F10) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Boundary value problems in the complex plane (30E25) Phase transitions (general) in equilibrium statistical mechanics (82B26) Random matrices (algebraic aspects) (15B52)

Related Items (21)

One-matrix differential reformulation of two-matrix models ⋮ Critical measures for vector energy: global structure of trajectories of quadratic differentials ⋮ On global fluctuations for non-colliding processes ⋮ A critical phenomenon in the two-matrix model in the quartic/quadratic case ⋮ Non-intersecting squared Bessel paths with one positive starting and ending point ⋮ Critical measures for vector energy: asymptotics of non-diagonal multiple orthogonal polynomials for a cubic weight ⋮ Orthogonal polynomials in the normal matrix model with a cubic potential ⋮ The global parametrix in the Riemann-Hilbert steepest descent analysis for orthogonal polynomials ⋮ Weakly admissible vector equilibrium problems ⋮ Weakly admissible vector equilibrium problems ⋮ Painlevé kernels in Hermitian matrix models ⋮ The tacnode Riemann-Hilbert problem ⋮ Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model ⋮ LARGE DEVIATIONS FOR A NON-CENTERED WISHART MATRIX ⋮ S-curves in polynomial external fields ⋮ Average characteristic polynomials of determinantal point processes ⋮ Random matrix model with external source and a constrained vector equilibrium problem ⋮ Central limit theorems for biorthogonal ensembles and asymptotics of recurrence coefficients ⋮ Global fluctuations for multiple orthogonal polynomial ensembles ⋮ Large \(n\) limit for the product of two coupled random matrices ⋮ Universality conjecture and results for a model of several coupled positive-definite matrices

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