Spectra of random Hermitian matrices with a small-rank external source: the critical and near-critical regimes

DOI10.1007/s10955-011-0409-2zbMath1241.82035arXiv1011.4983OpenAlexW3084237930MaRDI QIDQ664476

Robert J. Buckingham, Seung-Yeop Lee, Marco Bertola, Virgil U. Pierce

Publication date: 2 March 2012

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.4983

zbMATH Keywords

Riemann-Hilbert problemcritical phenomenaasymptotic analysisnonlinear steepest descent analysis\(r\)-Airy kernel

Mathematics Subject Classification ID

Critical phenomena in equilibrium statistical mechanics (82B27) Random matrices (algebraic aspects) (15B52) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items

Rank 1 real Wishart spiked model, Universality for random matrices with equi-spaced external source: a case study of a biorthogonal ensemble, The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source. I, Spectra of random Hermitian matrices with a small-rank external source: the supercritical and subcritical regimes, Random matrices with equispaced external source, The \(k\)-tacnode process, Spectral curves, variational problems and the Hermitian matrix model with external source, Boundaries of sine kernel universality for Gaussian perturbations of Hermitian matrices, Eigenvector distribution in the critical regime of BBP transition

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