# 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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