Gaussian fluctuation in random matrices

Ovidiu Costin, Joel L. Lebowitz

Research output: Contribution to journalArticlepeer-review

149 Scopus citations

Abstract

Let N(L) be the number of eigenvalues, in an interval of length L, of a matrix chosen at random from the Gaussian orthogonal, unitary, or symplectic ensembles of N by N matrices, in the limit N→. We prove that [N(L)-N(L)]/lnL has a Gaussian distribution when L→. This theorem, which requires control of all the higher moments of the distribution, elucidates numerical and exact results on chaotic quantum systems and on the statistics of zeros of the Riemann zeta function.

Original languageEnglish (US)
Pages (from-to)69-72
Number of pages4
JournalPhysical review letters
Volume75
Issue number1
DOIs
StatePublished - 1995

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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