The Riemann-Hilbert Approach to Double Scaling Limit of Random Matrix Eigenvalues Near the "Birth of a Cut" Transition

DOI10.1093/imrn/rnn042zbMath1149.15017arXiv0711.3208OpenAlexW2082978869MaRDI QIDQ3515964

Man Yue Mo

Publication date: 30 July 2008

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.3208

zbMATH Keywords

Riemann-Hilbert problemorthogonal polynomialdouble scaling limitrandom matrix ensembleDeift-Zhou steepest descent method

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52) Transition functions, generators and resolvents (60J35)

Related Items (12)

The Hermitian two matrix model with an even quartic potential ⋮ Universality in the two‐matrix model: a Riemann‐Hilbert steepest‐descent analysis ⋮ A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions ⋮ Nonintersecting Brownian bridges on the unit circle with drift ⋮ CLT for fluctuations of \(\beta \)-ensembles with general potential ⋮ Painlevé kernels in Hermitian matrix models ⋮ Asymptotics for Hankel determinants associated to a Hermite weight with a varying discontinuity ⋮ First colonization of a hard-edge in random matrix theory ⋮ Laguerre polynomials and transitional asymptotics of the modified Korteweg-de Vries equation for step-like initial data ⋮ Phase transitions and equilibrium measures in random matrix models ⋮ Splitting of a gap in the bulk of the spectrum of random matrices ⋮ Integrability-preserving regularizations of Laplacian Growth

This page was built for publication: The Riemann-Hilbert Approach to Double Scaling Limit of Random Matrix Eigenvalues Near the "Birth of a Cut" Transition