Date and time: 13 December 2000, 16:30

Venue: Room G2, School of Mathematical Sciences, Queen Mary, University of London

Speaker: Prof. Y. Fyodorov (Brunel University)

"Spectra of Random Contractions and Scattering Theory for Discrete-Time Systems"

Abstract: Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex eigenvalues of generic random matrices of such a type classifying deviations from unitarity by rank. We solve the problem completely by deriving the joint probability density of complex eigenvalues and calculating all correlation functions. In the limit of large matrix size the correlation functions acquire the universal form found earlier for weakly non-Hermitian random matrices.