Gaussian unitary ensemble eigenvalues and Riemann [Formula Presented] function zeros: A nonlinear equation for a new statistic

P. J. Forrester, A. M. Odlyzko

Research output: Contribution to journalArticlepeer-review

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Abstract

For infinite Gaussian unitary ensemble random matrices the probability density function [Formula Presented] for the nearest neighbor eignenvalue spacing (as distinct from the spacing between consecutive eigenvalues) is computed in terms of the solution of a certain nonlinear equation, which generalizes the σ form of the Painlevé [Formula Presented] equation. Comparison is made with the empirical value of [Formula Presented] for the zeros of the Riemann [Formula Presented] function on the critical line, including data from [Formula Presented] consecutive zeros near zero number [Formula Presented].

Original languageEnglish (US)
Pages (from-to)R4493-R4495
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume54
Issue number5
DOIs
StatePublished - 1996

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