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Trajectories in random minimaltransposition factorizations


Féray, Valentin; Kortchemski, Igor (2019). Trajectories in random minimaltransposition factorizations. ALEA: Latin American Journal of Probability and Mathematical Statistics, 16(1):759.

Abstract

We study random typical minimal factorizations of the n-cycle, which are factorizations of (1,...,n) as a product of n-1 transpositions, chosen uniformly at random. Our main result is, roughly speaking, a local convergence theorem for the trajectories of finitely many points in the factorization. The main tool is an encoding of the factorization by an edge and vertex-labelled tree, which is shown to converge to Kesten’s infinite Bienaymé-Galton-Watson tree with Poisson offspring distribution, uniform i.i.d. edge labels and vertex labels obtained by a local exploration algorithm.

Abstract

We study random typical minimal factorizations of the n-cycle, which are factorizations of (1,...,n) as a product of n-1 transpositions, chosen uniformly at random. Our main result is, roughly speaking, a local convergence theorem for the trajectories of finitely many points in the factorization. The main tool is an encoding of the factorization by an edge and vertex-labelled tree, which is shown to converge to Kesten’s infinite Bienaymé-Galton-Watson tree with Poisson offspring distribution, uniform i.i.d. edge labels and vertex labels obtained by a local exploration algorithm.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Uncontrolled Keywords:Statistics and Probability
Language:English
Date:1 January 2019
Deposited On:31 Oct 2019 09:52
Last Modified:29 Jul 2020 11:20
Publisher:Instituto nacional de matemática pura e aplicada
ISSN:1980-0436
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.30757/alea.v16-27

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