Math @ Duke

Publications [#244276] of Xin Zhou
Papers Published
 Deift, P; Its, A; Krasovsky, I; Zhou, X, The WidomDyson constant for the gap probability in random matrix theory,
Journal of Computational and Applied Mathematics, vol. 202 no. 1 SPECIAL ISSUE
(2007),
pp. 2647, ISSN 03770427 [doi]
(last updated on 2018/03/24)
Abstract: In the bulk scaling limit for the Gaussian Unitary Ensemble in random matrix theory, the probability that there are no eigenvalues in the interval (0, 2 s) is given by Ps = det (I  Ks), where Ks is the traceclass operator with kernel Ks (x, y) = frac(sin (x  y), π (x  y)) acting on L2 (0, 2 s). In the analysis of the asymptotic behavior of Ps as s → ∞, there is particular interest in the constant term known as the WidomDyson constant. We present a new derivation of this constant, which can be adapted to calculate similar critical constants in other problems arising in random matrix theory. © 2006 Elsevier B.V. All rights reserved.


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