Patterns in Sinai's walk

Mathematics – Probability

Scientific paper

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39 pages, 6 figures

Scientific paper

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.

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