Central Limit Theorem and recurrence for random walks in bistochastic random environments

TL;DR

This paper proves the annealed Central Limit Theorem for random walks in bistochastic environments with zero drift and establishes recurrence in low dimensions, using a novel approach that relaxes traditional conditions.

Contribution

It introduces a dynamicist's interpretation to prove the CLT under weaker conditions and demonstrates recurrence in dimensions two or less.

Findings

Proves annealed CLT for bistochastic environments with zero drift

Establishes recurrence for dimensions d ≤ 2

Uses a novel dynamicist's approach to weaken traditional assumptions

Abstract

We prove the annealed Central Limit Theorem for random walks in bistochastic random environments on $Z^d$ with zero local drift. The proof is based on a "dynamicist's interpretation" of the system, and requires a much weaker condition than the customary uniform ellipticity. Moreover, recurrence is derived for $d \le 2$.