On fluctuations of eigenvalues of random permutation matrices

Gérard Ben Arous; Kim Dang

doi:10.1214/13-AIHP569

On fluctuations of eigenvalues of random permutation matrices

Gérard Ben Arous, Kim Dang

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	620-647
Number of pages	28
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	51
Issue number	2
DOIs	https://doi.org/10.1214/13-AIHP569
State	Published - May 1 2015

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/13-AIHP569

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N2 - 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.

AB - 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.

KW - Infinitely divisible distributions

KW - Linear eigenvalue statistics

KW - Random matrices

KW - Random permutations

KW - Trapezoidal approximations

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On fluctuations of eigenvalues of random permutation matrices

Abstract

Keywords

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