The law of the iterated logarithm for a class of transient random walk in random environment

TL;DR

This paper establishes the law of the iterated logarithm for a class of transient random walks in random environments under the necessary ballisticity condition (T'), providing new insights into their asymptotic behavior.

Contribution

It proves the law of the iterated logarithm for transient random walks in random environments satisfying condition (T'), a key step in understanding their long-term behavior.

Findings

Law of the iterated logarithm holds under condition (T')

Provides a necessary condition for ballisticity in random walks

Advances theoretical understanding of random walk asymptotics

Abstract

There is a condition (T'), such that it is the necessary condition that a random walk in random environment is ballistic. Under this condition, we show the law of the iterated logarithm for a random walk in random environment.