Central limit theorem for peaks of a random permutation in a fixed conjugacy class of $S_n$

Jason Fulman, Gene B. Kim, Sangchul Lee

Published 2019-02-03Version 1

The number of peaks of a random permutation is known to be asymptotically normal. We give a new proof of this and prove a central limit theorem for the distribution of peaks in a fixed conjugacy class of the symmetric group. Our technique is to apply ``analytic combinatorics'' to study a complicated but exact generating function for peaks in a given conjugacy class.