The characteristic polynomial of a random permutation matrix at different points

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Dang, K.¹  Zeindler, D.² 

[1] Yale Univ, Dept Math, New Haven, CT 06511 USA

[2] Univ Bielefeld, Dept Math, D-33501 Bielefeld, Germany

关键词: Random matrices;    Symmetric groups;    Random permutations;    Multiplicative class functions;    Characteristic polynomial;    Limit theorems;   

DOI  :  10.1016/j.spa.2013.08.003

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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