We study one dimensional excited random walks (ERW) on iterated leftover environments. We prove a 0-1 law for directional transience and a law of large numbers for such environments under mild assumptions. We provide exact criteria for transience and positive speed of the walk in terms of the expected drift per site under stronger assumptions. This allows us to construct examples of stationary and ergodic environments on which ERW has positive speed that do not follow by trivial comparison to i.i.d. environments. A central ingredient is the introduction of the "Excited Mob" of k walkers on the same cookie environment.
Amir, G., Orenshtein, T. (2016). Excited Mob. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 126(2), 439-469 [10.1016/j.spa.2015.09.007].
Excited Mob
Orenshtein T.
2016
Abstract
We study one dimensional excited random walks (ERW) on iterated leftover environments. We prove a 0-1 law for directional transience and a law of large numbers for such environments under mild assumptions. We provide exact criteria for transience and positive speed of the walk in terms of the expected drift per site under stronger assumptions. This allows us to construct examples of stationary and ergodic environments on which ERW has positive speed that do not follow by trivial comparison to i.i.d. environments. A central ingredient is the introduction of the "Excited Mob" of k walkers on the same cookie environment.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
