Proof of universality of the Bessel kernel for chiral matrix models in the microscopic limit

S. Nishigaki

Published 1996-06-17, updated 1997-01-22Version 2

We prove the universality of correlation functions of chiral complex matrix models in the microscopic limit (N->\infty, z->0, N z=fixed) which magnifies the crossover region around the origin of the eigenvalue distribution. The proof exploits the fact that the three-term difference equation for orthogonal polynomials reduces into a universal second-order differential (Bessel) equation in the microscopic limit.