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First Colonization of a Hard-Edge in Random Matrix Theory

2009; Springer Science+Business Media; Volume: 31; Issue: 2 Linguagem: Inglês

10.1007/s00365-009-9052-4

1432-0940

Marco Bertola, S. Y. Lee,

Mathematical functions and polynomials

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.