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Article Dans Une Revue Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Année : 2017

Typical behavior of the harmonic measure in critical Galton-Watson trees

Résumé

We study the typical behavior of the harmonic measure of balls in large critical Galton-Watson trees whose offspring distribution has finite variance. The harmonic measure considered here refers to the hitting distribution of height n by simple random walk on a critical Galton-Watson tree conditioned to have height greater than n. We prove that, with high probability, the mass of the harmonic measure carried by a random vertex uniformly chosen from height n is approximately equal to n −λ , where the constant λ > 1 does not depend on the offspring distribution. This universal constant λ is equal to the first moment of the asymptotic distribution of the conductance of size-biased Galton-Watson trees minus 1.
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Dates et versions

hal-03891743 , version 1 (09-12-2022)

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Shen Lin. Typical behavior of the harmonic measure in critical Galton-Watson trees. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2017, 53 (2), pp.718-752. ⟨10.1214/15-AIHP734⟩. ⟨hal-03891743⟩
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