Distribution Functions for Random Variables for Ensembles of Positive Hermitian Matrices
- Cite this article as:
- Basor, E. Comm Math Phys (1997) 188: 327. doi: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.