Spectral statistics of permutation matrices | Zendy

Idan Oren | Zendy; Uzy Smilansky | Zendy

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Spectral statistics of permutation matrices

Author(s) -

Idan Oren,

Uzy Smilansky

Publication year - 2013

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2012.0508

Subject(s) - permutation (music) , mathematics , generating function , point (geometry) , divisor (algebraic geometry) , asymptotic analysis , variance (accounting) , permutation matrix , point process , combinatorics , statistics , physics , geometry , accounting , circulant matrix , acoustics , business

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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