The probability of long cycles in interchange processes

Gil Alon; Gady Kozma

doi:10.1215/00127094-2266018

The probability of long cycles in interchange processes

Gil Alon, Gady Kozma

Open University of Israel, Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

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 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 language	English
Pages (from-to)	1567-1585
Number of pages	19
Journal	Duke Mathematical Journal
Volume	162
Issue number	9
DOIs	https://doi.org/10.1215/00127094-2266018
State	Published - Jun 2013

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "The probability of long cycles in interchange processes",

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 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.",

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AB - 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.

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U2 - 10.1215/00127094-2266018

DO - 10.1215/00127094-2266018

M3 - مقالة

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SP - 1567

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JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

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The probability of long cycles in interchange processes

Abstract

All Science Journal Classification (ASJC) codes

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