Mock-Gaussian behaviour

Research output: Chapter in Book/Report/Conference proceedingChapter

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Department/unit(s)

Publication details

Title of host publicationRecent Perspectives in Random Matrix Theory and Number Theory
DatePublished - Jul 2005
Pages337-355
Number of pages19
PublisherCambridge University Press
Volume322
Original languageEnglish
ISBN (Print)9780521620581

Publication series

NameLondon Mathematical Society lecture Note Series

Abstract

We show that the moments of the smooth counting function of a set of points encodes the same information as the $n$-level density of these points. If the points are the eigenvalues of matrices taken from the classical compact groups with Haar measure, then we show that the first few moments of the smooth counting function are Gaussian, while the distribution is not. The same phenomenon occurs for smooth counting functions of the zeros of $L$--functions, and we give examples relating to each classical compact group. The advantage of calculating moments of the counting function is that combinatorially, they are far easier to handle than the $n$-level densities.

    Research areas

  • Pure Mathematics

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