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15 June 2013 The probability of long cycles in interchange processes
Gil Alon, Gady Kozma
Duke Math. J. 162(9): 1567-1585 (15 June 2013). DOI: 10.1215/00127094-2266018

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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Gil Alon. Gady Kozma. "The probability of long cycles in interchange processes." Duke Math. J. 162 (9) 1567 - 1585, 15 June 2013. https://doi.org/10.1215/00127094-2266018

Information

Published: 15 June 2013
First available in Project Euclid: 11 June 2013

zbMATH: 1269.82041
MathSciNet: MR3079255
Digital Object Identifier: 10.1215/00127094-2266018

Subjects:
Primary: 82C22
Secondary: 20B30 , ‎43A65 , 60B15

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 9 • 15 June 2013
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