The Characteristic Polynomial of a Random Permutation Matrix at Different Points
Probability
2013-09-17 v2 Number Theory
Abstract
We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show that the behavior at different points is independent in the limit and are asymptotically normal. Our methods enables us to study more general matrices, closely related to permutation matrices, and multiplicative class functions.
Cite
@article{arxiv.1110.4514,
title = {The Characteristic Polynomial of a Random Permutation Matrix at Different Points},
author = {Kim Dang and Dirk Zeindler},
journal= {arXiv preprint arXiv:1110.4514},
year = {2013}
}
Comments
30 pages, 2 figures. Differences to Version 1: We have improved the presentation and add some references Stochastic Processes and their Applications, 2013