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.
First Colonization of a Hard-Edge in Random Matrix Theory / Bertola, M.; Lee, S. Y.. - In: CONSTRUCTIVE APPROXIMATION. - ISSN 0176-4276. - 31:2(2010), pp. 231-257. [10.1007/s00365-009-9052-4]
First Colonization of a Hard-Edge in Random Matrix Theory
Bertola, M.;
2010-01-01
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.File in questo prodotto:
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