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.
Domaines
Probabilités [math.PR]Origine | Fichiers éditeurs autorisés sur une archive ouverte |
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