The speed of a biased walk on a Galton–Watson tree without leaves is monotonic with respect to progeny distributions for high values of bias
Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 1, pp. 304-318.

Nous considérons des marches aléatoires biaisées sur deux arbres de Galton–Watson sans feuilles GW (P 1 ) et GW (P 2 ) ayant des lois de reproduction respectivement P 1 et P 2 , deux lois supportées par les entiers positifs telles que P 1 domine stochastiquement P 2 . Nous prouvons que la vitesse de la marche sur GW (P 1 ) est supérieure ou égale á celle sur GW (P 2 ) si le biais est plus grand qu’un seuil dépendant de P 1 et P 2 . Ceci répond partiellement á une question posée par Ben Arous, Fribergh et Sidoravicius (Comm. Pure Appl. Math. 67 (2014) 519–530).

Consider biased random walks on two Galton–Watson trees without leaves having progeny distributions P 1 and P 2 ( GW (P 1 ) and GW (P 2 )) where P 1 and P 2 are supported on positive integers and P 1 dominates P 2 stochastically. We prove that the speed of the walk on GW (P 1 ) is bigger than the same on GW (P 2 ) when the bias is larger than a threshold depending on P 1 and P 2 . This partially answers a question raised by Ben Arous, Fribergh and Sidoravicius (Comm. Pure Appl. Math. 67 (2014) 519–530).

DOI : 10.1214/13-AIHP573
Classification : 60K37, 60J80, 60G50
Mots clés : random walk in random environment, Galton–Watson tree, speed, stochastic domination
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Mehrdad, Behzad; Sen, Sanchayan; Zhu, Lingjiong. The speed of a biased walk on a Galton–Watson tree without leaves is monotonic with respect to progeny distributions for high values of bias. Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 1, pp. 304-318. doi : 10.1214/13-AIHP573. http://archive.numdam.org/articles/10.1214/13-AIHP573/

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