Cycle structure of random permutations with cycle weights

Nicholas M. Ercolani, Daniel Ueltschi

Published 2011-02-23, updated 2012-03-19Version 2

We investigate the typical cycle lengths, the total number of cycles, and the number of finite cycles in random permutations whose probability involves cycle weights. Typical cycle lengths and total number of cycles depend strongly on the parameters, while the distributions of finite cycles are usually independent Poisson random variables.