Distribution Functions for Random Variables for Ensembles of positive Hermitian Matrices

Details Distribution Functions for Random Variables for Ensembles of positive Hermitian Matrices Distribution Functions for Random Variables for Ensembles of positive Hermitian Matrices

2001-07-20

arxiv.org/abs/math/0107154v1

Communications in Mathematical Physics 188, 327-350

Mathematics

Functional Analysis

Scientific paper

10.1007/s002200050167

Distribution functions for random variables that depend on a parameter are computed asymptotically for ensembles of positive Hermitian matrices. The inverse Fourier transform of the distribution is shown to be a Fredholm determinant of a certain operator that is an analogue of a Wiener-Hopf operator. The asymptotic formula shows that up to the terms of order $o(1)$, the distributions are Gaussian.

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