First colonization of a hard-edge in random matrix theory

Abstract

We describe the spectral statistics of the first finite number of eigenvalues in a newly-forming band on the hard-edge of the spectrum of a random Hermitean matrix model. It is found that in a suitable scaling regime, they are described by the same spectral statistics of a finite-size Laguerre-type matrix model. The method is rigorously based on the Riemann-Hilbert analysis of the corresponding orthogonal polynomials.

22 pages, 7 figures

References in corpus (2)

• The birth of a cut in unitary random matrix ensembles
• The Riemann-Hilbert approach to double scaling limit of random matrix eigenvalues near the "birth of a cut" transition