Excited Mob

Gideon Amir and Tal Orenshtein

Stochastic Processes and their Applications, 2016, vol. 126, issue 2, 439-469

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.

Keywords: Excited random walk; Cookie walk; Abelianness; Recurrence; Transience; Zero–one laws; Law of large numbers; Limit theorems; Random environment; Regeneration structure (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414915002252
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:2:p:439-469

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2015.09.007

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().