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

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…