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2020 A product of invariant random permutations has the same small cycle structure as uniform
Slim Kammoun Kammoun, Mylène Maïda
Electron. Commun. Probab. 25: 1-14 (2020). DOI: 10.1214/20-ECP334

Abstract

We use moment method to understand the cycle structure of the composition of two independent invariant permutations. We prove that under a good control on fixed points and cycles of length $2$, the limiting joint distribution of the number of small cycles is the same as in the uniform case i.e. for any positive integer $k$, the number of cycles of length $k$ converges to the Poisson distribution with parameter $\frac {1}{k}$ and is asymptotically independent of the number of cycles of length $k'\neq k$.

Citation

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Slim Kammoun Kammoun. Mylène Maïda. "A product of invariant random permutations has the same small cycle structure as uniform." Electron. Commun. Probab. 25 1 - 14, 2020. https://doi.org/10.1214/20-ECP334

Information

Received: 21 October 2019; Accepted: 5 July 2020; Published: 2020
First available in Project Euclid: 8 August 2020

zbMATH: 07252777
Digital Object Identifier: 10.1214/20-ECP334

Subjects:
Primary: 05A05, 05A16, 60B20, 60C05, 60F05

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