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

Bar-Ilan University, Weizmann Institute of Science

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

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

Keywords

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

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/14-AIHP615

Cite this

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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.",

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

author = "Gideon Amir and Noam Berger and Tal Orenshtein",

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AB - 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.

KW - Cookie walk

KW - Directional transience

KW - Excited random walk

KW - Law of large numbers

KW - Limit theorem

KW - Random environment

KW - Recurrence

KW - Zero-one law

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M3 - مقالة

SN - 0246-0203

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EP - 57

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

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IS - 1

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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