The probability of long cycles in interchange processes

Gil Alon; Gady Kozma

doi:10.1215/00127094-2266018

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arXiv · 1009.3723

The probability of long cycles in interchange processes

Gil Alon·Gady Kozma

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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.

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Gil Alon, Gady Kozma. 2010-09-20. The probability of long cycles in interchange processes. https://doi.org/10.1215/00127094-2266018

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