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

preprint2018arXivOpen access

Abstract

We prove a ballistic strong law of large numbers and an invariance principle for random walks in strong mixing environments, under condition (T)(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.

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