The Widom-Dyson constant for the gap probability in random matrix theory

Details The Widom-Dyson constant for the gap probability in random matrix theory The Widom-Dyson constant for the gap probability in random matrix theory

2006-01-22

arxiv.org/abs/math/0601535v1

Mathematics

Functional Analysis

31 pages, 4 figures

Scientific paper

In this paper we consider an asymptotic question in the theory of the Gaussian Unitary Ensemble of random matrices. In the bulk scaling limit, the probability that there are no eigenvalues in the interval (0,2s) is given by P_s=det(I-K_s), where K_s is the trace-class operator with kernel K_s(x,y)={sin(x-y)}/{\pi(x-y)} acting on L^2(0,2s). We are interested particularly in the behavior of P_s as s tends to infinity...

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