Distribution Functions for Random Variables for Ensembles of Positive Hermitian Matrices
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- Basor, E. Comm Math Phys (1997) 188: 327. doi:10.1007/s002200050167
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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.