On fluctuations of eigenvalues of random permutation matrices

Research output: Contribution to journalArticle

Abstract

Smooth linear statistics of random permutation matrices, sampled under a general Ewens distribution, exhibit an interesting non-universality phenomenon. Though they have bounded variance, their fluctuations are asymptotically non-Gaussian but infinitely divisible. The fluctuations are asymptotically Gaussian for less smooth linear statistics for which the variance diverges. The degree of smoothness is measured in terms of the quality of the trapezoidal approximations of the integral of the observable.

Original languageEnglish (US)
Pages (from-to)620-647
Number of pages28
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume51
Issue number2
DOIs
StatePublished - May 1 2015

Fingerprint

Permutation Matrix
Random Permutation
Random Matrices
Fluctuations
Statistics
Eigenvalue
Infinitely Divisible
Diverge
Smoothness
Approximation
Eigenvalues
Integral

Keywords

  • Infinitely divisible distributions
  • Linear eigenvalue statistics
  • Random matrices
  • Random permutations
  • Trapezoidal approximations

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

On fluctuations of eigenvalues of random permutation matrices. / Arous, Gérard Ben; Dang, Kim.

In: Annales de l'institut Henri Poincare (B) Probability and Statistics, Vol. 51, No. 2, 01.05.2015, p. 620-647.

Research output: Contribution to journalArticle

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