Universal Correlations Near a Singularity of Random Matrix Spectrum

Abstract

Asymptotic correlation functions of the eigenvalues in the limit of large dimension of random matrices are evaluated for two models related to the Jacobi polynomials. One of the models is a generalization of Dyson's circular ensemble. Both models show identical unfolded correlations near a singularity of the spectrum. A previously unnoticed universal behavior of random matrix ensembles near a singularity is discussed.