### 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 | |

State | Published - May 1 2015 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Annales de l'institut Henri Poincare (B) Probability and Statistics*, vol. 51, no. 2, pp. 620-647. https://doi.org/10.1214/13-AIHP569

}

TY - JOUR

T1 - On fluctuations of eigenvalues of random permutation matrices

AU - Arous, Gérard Ben

AU - Dang, Kim

PY - 2015/5/1

Y1 - 2015/5/1

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

UR - http://www.scopus.com/inward/record.url?scp=84927667436&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84927667436&partnerID=8YFLogxK

U2 - 10.1214/13-AIHP569

DO - 10.1214/13-AIHP569

M3 - Article

AN - SCOPUS:84927667436

VL - 51

SP - 620

EP - 647

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

SN - 0246-0203

IS - 2

ER -