The Generating Function for the Airy Point Process and a System of Coupled Painlevé II Equations

DOI10.1111/sapm.12209zbMath1419.37063arXiv1708.03481OpenAlexW2789901348MaRDI QIDQ5374594

Tom Claeys, Antoine Doeraene

Publication date: 14 September 2018

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.03481

zbMATH Keywords

asymptotic behaviorRiemann-Hilbert problemFredholm determinantPainlevé II equationLax pairAiry point processTracy-Widom-type formula

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) NLS equations (nonlinear Schrödinger equations) (35Q55) Random matrices (algebraic aspects) (15B52) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

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