Trajectories in random minimal transposition factorizations - Centre de mathématiques appliquées (CMAP)
Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2019

Trajectories in random minimal transposition factorizations

Résumé

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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Dates et versions

hal-02352601 , version 1 (06-01-2025)

Identifiants

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Valentin Féray, Igor Kortchemski. Trajectories in random minimal transposition factorizations. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2019, 16 (1), pp.759. ⟨10.30757/ALEA.v16-27⟩. ⟨hal-02352601⟩
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