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

Abstract

The speed $v(\beta )$ of a $\beta$-biased random walk on a Galton-Watson tree without leaves is increasing for $\beta \ge 717$.

12 pages

References in corpus (2)

• Speed of the biased random walk on a Galton--Watson tree
• Randomly biased walks on subcritical trees

Cited by in corpus (2)

• The maximal potential energy of biased random walks on trees
• 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