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On the monotonicity of the speed of biased random walk on a Galton-Watson tree without leaves

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We will present different results related to the speed of biased random walks in random environments. Our main focus will be on a recent paper (by Ben Arous, Fribergh and Sidoravicius) proving that the speed of the biased random walk on a Galton-Watson tree without leaves is increasing for high biases. This partially addresses a question asked by Lyons, Pemantle and Peres.

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