Fixed points and cycle structure of random permutations

Sumit Mukherjee

Published 2015-09-15Version 1

Using the recently developed notion of permutation limits this paper derives the limiting distribution of the number of fixed points and the cycle structure of any convergent sequence of random permutations, under mild regularity conditions. In particular this covers random permutations generated from Mallows Model with Kendall's Tau, as well as a class of exponential families introduced in [13].