Diffusion on GL(N, C)/U(N) and Eigenvalue Density for N→ ∞ Limit

Abstract

Studied is the probability density of random hermitian matrices which is naturally obtained by the diffusion on GL(N, C)/U(N). The exact expression for the n-point correlation is obtained by the orthogonal polynomial method. The eigenvalue density is evaluated in the large N limit and the result is compared with the semi-circle law of the Gaussian Unitary Ensemble (GUE). In the analysis, the method developed by Kazakov is made use of.