# A proof of the Lyons-Pemantle-Peres monotonicity conjecture for high biases

@inproceedings{Arous2011APO,
title={A proof of the Lyons-Pemantle-Peres monotonicity conjecture for high biases},
author={G{\'e}rard Ben Arous and Alexander Fribergh and Vladas Sidoravicius},
year={2011}
}
• Published 2011
The speed $v(\beta)$ of a $\beta$-biased random walk on a Galton-Watson tree without leaves is increasing for $\beta \geq 717$.

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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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## A monotonicity property for random walk in a partially random environment

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