, Volume 188, Issue 2, pp 327-350

Distribution Functions for Random Variables for Ensembles of Positive Hermitian Matrices

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Abstract:

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.

Received: 5 November 1996 / Accepted: 8 January 1997