Consider biased random walks on two Galton-Watson trees without leaves having progeny distributions P1 and P2 (GW(P1) and GW(P2)) where P1 and P2 are supported on positive integers and P1 dominates P2 stochastically. We prove that the speed of the walk on GW(P1) is bigger than the same on GW(P2) when the bias is larger than a threshold depending on P1 and P2. This partially answers a question raised by Ben Arous, Fribergh and Sidoravicius (Comm. Pure Appl. Math. 67 (2014) 519-530).
|Original language||English (US)|
|Number of pages||15|
|Journal||Annales de l'institut Henri Poincare (B) Probability and Statistics|
|State||Published - Feb 1 2015|
Bibliographical notePublisher Copyright:
© Association des Publications de l'Institut Henri Poincaré, 2015.
- Galton-Watson tree
- Random walk in random environment
- Stochastic domination