The Characteristic Polynomial of a Random Permutation Matrix at Different Points

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.

arXiv comment30 pages, 2 figures. Differences to Version 1: We have improved the presentation and add some references Stochastic Processes and their Applications, 2013

References in corpus (5)

• Gaussian Fluctuation in Random Matrices
• Cycle structure of random permutations with cycle weights
• On the number of cycles in a random permutation
• Random permutation matrices under the generalized Ewens measure
• Large cycles and a functional central limit theorem for generalized weighted random permutations

Cited by in corpus (1)

• Eigenvalue Fluctuations of Symmetric Group Permutation Representations on k-tuples and k-subsets