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

Behzad Mehrdad; Sanchayan Sen; Lingjiong Zhu

doi:10.1214/13-AIHP573

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

Behzad Mehrdad, Sanchayan Sen, Lingjiong Zhu

Mathematics

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Abstract

Consider biased random walks on two Galton-Watson trees without leaves having progeny distributions P₁ and P₂ (GW(P₁) and GW(P₂)) where P₁ and P₂ are supported on positive integers and P₁ dominates P₂ stochastically. We prove that the speed of the walk on GW(P₁) is bigger than the same on GW(P₂) when the bias is larger than a threshold depending on P₁ and P₂. This partially answers a question raised by Ben Arous, Fribergh and Sidoravicius (Comm. Pure Appl. Math. 67 (2014) 519-530).

Original language	English (US)
Pages (from-to)	304-318
Number of pages	15
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	51
Issue number	1
DOIs	https://doi.org/10.1214/13-AIHP573
State	Published - Feb 1 2015

Bibliographical note

Publisher Copyright:
© Association des Publications de l'Institut Henri Poincaré, 2015.

Keywords

Galton-Watson tree
Random walk in random environment
Speed
Stochastic domination

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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. / Mehrdad, Behzad; Sen, Sanchayan; Zhu, Lingjiong.
In: Annales de l'institut Henri Poincare (B) Probability and Statistics, Vol. 51, No. 1, 01.02.2015, p. 304-318.

Research output: Contribution to journal › Article › peer-review

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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

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