Spectral statistics of permutation matrices

We compute the mean two-point spectral form factor and the spectral number variance for permutation matrices of large order. The two-point correlation function is expressed in terms of generalized divisor functions, which are frequently discussed in number theory. Using classical results from number...

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Bibliographic Details
Published inPhilosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 372; no. 2007; pp. 1 - 10
Main Authors Oren, Idan, Smilansky, Uzy
Format Journal Article
LanguageEnglish
Published Royal Society 28.01.2014
Subjects
Data smoothing
Eigenvalues
Integers
Mathematical functions
Mathematical lattices
Mathematical permutation
Matrices
Number theory
Spectral graph theory
Statistical variance
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ISSN1364-503X

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Summary:We compute the mean two-point spectral form factor and the spectral number variance for permutation matrices of large order. The two-point correlation function is expressed in terms of generalized divisor functions, which are frequently discussed in number theory. Using classical results from number theory and casting them in a convenient form, we derive expressions which include the leading and next to leading terms in the asymptotic expansion, thus providing a new point of view on the subject, and improving some known results.
ISSN:1364-503X