Spectra of Random Matrices Close to Unitary and Scattering Theory for Discrete-Time Systems
Yan V. Fyodorov
Abstract
We analyze statistical properties of complex eigenvalues of random matrices A close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. Deviation from unitarity are characterized by rank M and eigenvalues Ti, i=1,...,M of the matrix T= 1-AA. For the case M=1 we solve the problem completely by deriving the joint probability density of eigenvalues and calculating all n- point correlation functions. For a general case we present the correlation function of secular determinants.
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