Gap probability in the spectrum of random matrices and asymptotics of polynomials orthogonal on an arc of the unit circle

dc.creatorKrasovsky, I. V.
dc.date2004-01-20
dc.date2004-04-22
dc.date.accessioned2026-07-07T05:04:42Z
dc.date.available2026-07-07T05:04:42Z
dc.descriptionWe obtain uniform asymptotics for polynomials orthogonal on a fixed and varying arc of the unit circle with a positive analytic weight function. We also complete the proof of the large $s$ asymptotic expansion for the Fredholm determinant with the kernel $\sin z/(πz)$ on the interval $[0,s]$, verifying a conjecture of Dyson for the constant term in the expansion. In the Gaussian Unitary Ensemble of random matrices, this determinant describes the probability for an interval of length $s$ in the bulk scaling limit to be free from the eigenvalues.
dc.description20 pages, 1 figure, small changes
dc.identifierhttps://arxiv.org/abs/math/0401258
dc.identifierhttp://arxiv.org/abs/math/0401258
dc.identifierInt.Math.Res.Not. 2004 (2004), no.25, 1249-1272
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69906
dc.subjectFunctional Analysis
dc.subjectMathematical Physics
dc.titleGap probability in the spectrum of random matrices and asymptotics of polynomials orthogonal on an arc of the unit circle
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