Zero-one law for directional transience of one dimensional excited random walks

Gideon Amir; Noam Berger; Tal Orenshtein

doi:10.1214/14-AIHP615

Zero-one law for directional transience of one dimensional excited random walks

Gideon Amir, Noam Berger, Tal Orenshtein

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

The probability that a one dimensional excited random walk in stationary ergodic and elliptic cookie environment is transient to the right (left) is either zero or one. This solves a problem posed by Kosygina and Zerner (Bull. Inst. Math. Acad. Sin. (N.S.) 8 (2013) 105-157). As an application, a law of large numbers holds in these conditions.

Original language	English
Pages (from-to)	47-57
Number of pages	11
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	52
Issue number	1
DOIs	https://doi.org/10.1214/14-AIHP615
State	Published - Feb 2016

Bibliographical note

Publisher Copyright:
© 2016 Association des Publications de l'Institut Henri Poincare.

Keywords

Cookie walk
Directional transience
Excited random walk
Law of large numbers
Limit theorem
Random environment
Recurrence
Zero-one law

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10.1214/14-AIHP615

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Zero-one law for directional transience of one dimensional excited random walks

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Keywords

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