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