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The characteristic polynomial of a random permutation matrix at different points

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>01/2014
<mark>Journal</mark>Stochastic Processes and their Applications
Issue number1
Volume124
Number of pages29
Pages (from-to)411-439
Publication StatusPublished
<mark>Original language</mark>English

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 enable us to study also the wreath product of permutation matrices and diagonal matrices with i.i.d. entries and more general class functions on the symmetric group with a multiplicative structure.