The probability of long cycles in interchange processes

Gil Alon, Gady Kozma

Research output: Contribution to journalArticlepeer-review


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 us to study the 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.

Original languageEnglish
Pages (from-to)1567-1585
Number of pages19
JournalDuke Mathematical Journal
Issue number9
StatePublished - Jun 2013


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