Electronic Journal of Probability

Fixed points and cycle structure of random permutations

Sumit Mukherjee

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Using the recently developed notion of permutation limits this paper derives the limiting distribution of the number of fixed points and cycle structure for any convergent sequence of random permutations, under mild regularity conditions. In particular this covers random permutations generated from Mallows Model with Kendall’s Tau, $\mu $ random permutations introduced in [11], as well as a class of exponential families introduced in [15].

Article information

Electron. J. Probab., Volume 21 (2016), paper no. 40, 18 pp.

Received: 12 October 2015
Accepted: 24 May 2016
First available in Project Euclid: 15 June 2016

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Primary: 05A05: Permutations, words, matrices 60C05: Combinatorial probability 60F05: Central limit and other weak theorems

combinatorial probability Mallows model permutation limit fixed points cycle structure

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Mukherjee, Sumit. Fixed points and cycle structure of random permutations. Electron. J. Probab. 21 (2016), paper no. 40, 18 pp. doi:10.1214/16-EJP4622. https://projecteuclid.org/euclid.ejp/1465991838

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