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

Abstract

We prove the universality of correlation functions of chiral complex matrix models in the microscopic limit ( N → ∞, z → 0, Nz = 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.