On slowdown and speedup of transient random walks in random environment

Alexander Fribergh, Nina Gantert, Serguei Popov

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11 Scopus citations

Abstract

We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(nκ) from the origin, κ ∈ (0, 1). We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order O(nν 0 from the origin, ν0 ∈ (0, κ)), and speedup (at time n, the particle is at a distance of order nν 1 from the origin, ν1 ∈ (κ, 1)), for the current location of the particle and for the hitting times. Also, we study probabilities of backtracking: at time n, the particle is located around (-nν), thus making an unusual excursion to the left. For the slowdown, our results are valid in the ballistic case as well.

Original languageEnglish
Pages (from-to)43-88
Number of pages46
JournalProbability Theory and Related Fields
Volume147
Issue number1
DOIs
StatePublished - Feb 2010
Externally publishedYes

Keywords

  • Moderate deviations
  • Slowdown
  • Speedup
  • Transience

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