The Characteristic Polynomial of a Random Permutation Matrix at Different Points
arXiv:1110.4514 · doi:10.1016/j.spa.2013.08.003
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.
30 pages, 2 figures. Differences to Version 1: We have improved the presentation and add some references Stochastic Processes and their Applications, 2013