Lyapunov exponents of random walks in small random potential: The upper bound

Thomas Mountford, Jean Christophe Mourrat

Research output: Contribution to journalArticle

Abstract

We consider the simple random walk on Zd evolving in a random i.i.d. potential taking values in [0;+∞). The potential is not assumed integrable, and can be rescaled by a multiplicative factor λ > 0. Completing the work started in a companion paper, we give the asymptotic behaviour of the Lyapunov exponents for d ≥ 3, both annealed and quenched, as the scale parameter λ tends to zero.

Original languageEnglish (US)
Article number49
Pages (from-to)1-18
Number of pages18
JournalElectronic Journal of Probability
Volume20
DOIs
StatePublished - 2015

Keywords

  • Anderson model
  • Lyapunov exponents
  • Random walk in random potential

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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