From gap probabilities in random matrix theory to eigenvalue expansions

DOI10.1088/1751-8113/49/7/075204zbMath1342.60007arXiv1509.07159OpenAlexW3106457563MaRDI QIDQ2994521

Thomas Bothner

Publication date: 2 August 2016

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.07159

zbMATH Keywords

Riemann-Hilbert problemspectrum analysisDeift-Zhou nonlinear steepest descent methodtransition asymptoticsintegrable integral operators

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Phase transitions (general) in equilibrium statistical mechanics (82B26) Asymptotics of solutions to integral equations (45M05) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Eigenvalue problems for integral equations (45C05)

Related Items (9)

On the deformed Pearcey determinant ⋮ Lower tail of the KPZ equation ⋮ Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel ⋮ On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo-Miwa-Ueno differential ⋮ Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain ⋮ Gap Probability at the Hard Edge for Random Matrix Ensembles with Pole Singularities in the Potential ⋮ Large deformations of the Tracy-Widom distribution. I: Non-oscillatory asymptotics ⋮ Some open problems in random matrix theory and the theory of integrable systems. II ⋮ The sine process under the influence of a varying potential

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