Constructive Approximation

, Volume 31, Issue 2, pp 231–257 | Cite as

First Colonization of a Hard-Edge in Random Matrix Theory

Article

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, a phenomenon also known as the “birth of a cut” near a hard-edge. 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.

Keywords

Orthogonal polynomials Random matrix theory Schlesinger transformations Riemann–Hilbert problems 

Mathematics Subject Classification (2000)

05E35 15A52 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsConcordia UniversityMontréalCanada
  2. 2.Centre de Recherches MathématiquesUniversité de MontréalMontréalCanada

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