The Widom-Dyson constant for the gap probability in random matrix theory
Abstract
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 Ps=det(I-Ks), where Ks is the trace-class operator with kernel Ks(x,y)=sin(x-y)/π(x-y) acting on L2(0,2s). We are interested particularly in the behavior of Ps as s tends to infinity...
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