Monotonicity of the speed for biased random walk on Galton-Watson tree

2016/10/26 by He, Song, Longmin, Wang, Kainan, Xiang
#60J15 #60J80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1610.08151

Abstract

Ben Arous, Fribergh and Sidoravicius \citeGAV2014 proved that speed of biased random walk RW_λ on a Galton-Watson tree without leaves is strictly decreasing for λ≤ (m₁)/(1160), where m₁ is minimal degree of the Galton-Watson tree. And A"ıdékon \citeEA2013 improved this result to λ≤ (1)/(2). In this paper, we prove that for the RW_λ on a Galton-Watson tree without leaves, its speed is strictly decreasing for λ∈ [0,(m₁)/(1+√(1-(1)/(m₁)))] when m₁≥ 2; and we owe the proof to A"ıdékon \citeEA2013.

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