Duke Mathematical Journal

The probability of long cycles in interchange processes

Gil Alon and Gady Kozma

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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.

Article information

Duke Math. J., Volume 162, Number 9 (2013), 1567-1585.

First available in Project Euclid: 11 June 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 82C22: Interacting particle systems [See also 60K35]
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization 43A65: Representations of groups, semigroups, etc. [See also 22A10, 22A20, 22Dxx, 22E45] 20B30: Symmetric groups


Alon, Gil; Kozma, Gady. The probability of long cycles in interchange processes. Duke Math. J. 162 (2013), no. 9, 1567--1585. doi:10.1215/00127094-2266018. https://projecteuclid.org/euclid.dmj/1370955539

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