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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Veröffentlicht in:	Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2014-01, Vol.372 (2007), p.1-10
Hauptverfasser:	Oren, Idan, Smilansky, Uzy
Format:	Artikel
Sprache:	eng
Schlagworte:	Data smoothing Eigenvalues Integers Mathematical functions Mathematical lattices Mathematical permutation Matrices Number theory Spectral graph theory Statistical variance
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description	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.
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subjects	Data smoothing Eigenvalues Integers Mathematical functions Mathematical lattices Mathematical permutation Matrices Number theory Spectral graph theory Statistical variance
title	Spectral statistics of permutation matrices
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