On the Transient (T) condition for Random Walk in Strong Mixing Environment

Abstract

We prove a ballistic strong law of large numbers and an invariance principle for random walks in strong mixing environments, under condition $(T)$ of Sznitman (cf. \cite{Sz01}). This weakens by first time the Kalikow ballistic assumption in mixing and proves finite moments of arbitrary order for the approximate regeneration time of \cite{CZ02}. The main technical tool in the proof is the introduction of renormalization schemes, which had only been considered for i.i.d. environments.

First revision

References in corpus (4)

• The Point of View of the Particle on the Law of Large Numbers for Random Walks in a Mixing Random Environment
• Almost sure functional central limit theorem for ballistic random walk in random environment
• Asymptotic direction for random walks in mixing random environments
• Almost exponential decay for the exit probability from slabs of ballistic RWRE

Cited by in corpus (1)

• A proof of Sznitman's conjecture about ballistic RWRE