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.
| Original language | English |
|---|---|
| Pages (from-to) | 439-469 |
| Number of pages | 31 |
| Journal | Stochastic Processes and their Applications |
| Volume | 126 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Feb 2016 |
Bibliographical note
Funding Information:We thank Noam Berger and Gady Kozma for useful discussions. We thank the anonymous referees for their thorough reading of the earlier version of this manuscript and their useful comments which helped to improve this paper. The research of G.A. was supported by the Israel Science Foundation grant ISF 1471/11 and by a young GIF grant from the German Israeli foundation . The research of T.O. was partly supported by the Israel Science Foundation.
Publisher Copyright:
© 2015 Elsevier B.V. 2015 Elsevier B.V. All rights reserved.
Keywords
- Abelianness
- Cookie walk
- Excited random walk
- Law of large numbers
- Limit theorems
- Random environment
- Recurrence
- Regeneration structure
- Transience
- Zero one laws