Trajectories in random minimal transposition factorizations

Valentin Féray; Igor Kortchemski

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arXiv · 1810.07586

Trajectories in random minimal transposition factorizations

Valentin Féray·Igor Kortchemski

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Abstract

We study random typical minimal factorizations of the $n$-cycle, which are factorizations of $(1, \ldots,n)$ 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 Bienaym\'e-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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Valentin Féray, Igor Kortchemski. 2018-10-17. Trajectories in random minimal transposition factorizations. https://arxiv.org/abs/1810.07586

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