Fixed points and cycle structure of random permutations

Abstract

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].

Minor updates in presentation. The definition of cycles is now corrected, and Theorem 1.4 has been updated to reflect these changes. Electron. J. Probab. 21 (2016), paper no. 40

References in corpus (1)

• Exchangeable pairs and Poisson approximation

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