Lyapunov exponents, shape theorems and large deviations for the random walk in random potential

Jean Christophe Mourrat

Research output: Contribution to journalArticle

Abstract

We consider the simple random walk on ℤd evolving in a potential of independent and identically distributed random variables taking values in [0,+∞]. We give optimal conditions for the existence of the quenched point-to-point Lyapunov exponent, and for different versions of a shape theorem. The method of proof applies as well to first-passage percolation, and builds up on an approach of Cox and Durrett (1981). The weakest form of shape theorem holds whenever the set of sites with finite potential percolates. Under this condition, we then show the existence of the quenched point-to-hyperplane Lyapunov exponent, and give a large deviation principle for the walk under the quenched weighted measure.

Original languageEnglish (US)
Pages (from-to)165-211
Number of pages47
JournalAlea
Volume9
Issue number1
StatePublished - 2012

Keywords

  • First-passage percolation
  • Large deviations
  • Lyapunov exponents
  • Random walk in random potential
  • Shape theorem

ASJC Scopus subject areas

  • Statistics and Probability

Fingerprint Dive into the research topics of 'Lyapunov exponents, shape theorems and large deviations for the random walk in random potential'. Together they form a unique fingerprint.

  • Cite this