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Distribution Functions for Random Variables for Ensembles of positive Hermitian Matrices
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 ,
the distributions are Gaussian
Asymptotics of determinants of Bessel operators
In this paper we determine the asymptotics of the determinant of Bessel
operators for sufficiently smooth generating functions. These operators are
similar to Wiener-Hopf operators with the Fourier transform replaced by the
Hankel transform and thus the asymptotics of the determinanst are similar to
the well-known Szeg\"o-Akhiezer-Kac formula for truncated Wiener-Hopf
determinants. In order to compute the above, we also show that the Bessel
operators differ from the Wiener-Hopf by a Hilbert-Schmidt operator
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