Patterns in Sinai’s walk

Dimitris Cheliotis; Bálint Virág

doi:10.1214/11-AOP724

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Home > Journals > Ann. Probab. > Volume 41 > Issue 3B > Article

May 2013 Patterns in Sinai’s walk

Dimitris Cheliotis, Bálint Virág

Ann. Probab. 41(3B): 1900-1937 (May 2013). DOI: 10.1214/11-AOP724

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Abstract

Sinai’s random walk in random environment shows interesting patterns on the exponential time scale. We characterize the patterns that appear on infinitely many time scales after appropriate rescaling (a functional law of iterated logarithm). The curious rate function captures the difference between one-sided and two-sided behavior.