The probability of long cycles in interchange processes
Probability
2019-12-19 v3 Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1009.3723,
title = {The probability of long cycles in interchange processes},
author = {Gil Alon and Gady Kozma},
journal= {arXiv preprint arXiv:1009.3723},
year = {2019}
}
Comments
14 pages, 3rd version adds more detailed description of Toth's conjecture