%0 Journal Article
%T The probability of long cycles in interchange processes
%A Gil Alon
%A Gady Kozma
%J Mathematics
%D 2010
%I arXiv
%X We examine the number of cycles of length k in a permutation, as a function on the symmetric group. We write it explicitly as a combination of characters of irreducible representations. This allows to study formation of long cycles in the interchange process, including a precise formula for the probability that the permutation is one long cycle at a given time t, and estimates for the cases of shorter cycles.
%U http://arxiv.org/abs/1009.3723v3