# Almost sure functional central limit theorem for non-nestling random walk in random environment

## TL;DR

This paper proves an almost sure functional central limit theorem for non-nestling random walks in random environments, showing that the scaled walk converges to a Brownian motion under broad conditions.

## Contribution

It establishes an invariance principle for non-nestling random walks in random environments with exponential moment conditions, highlighting subdiffusive behavior of the quenched mean.

## Key findings

- Invariance principle holds under almost every environment.
- Quenched mean exhibits subdiffusive behavior.
- Results apply to walks with exponential moment conditions.

## Abstract

We consider a non-nestling random walk in a product random environment. We assume an exponential moment for the step of the walk, uniformly in the environment. We prove an invariance principle (functional central limit theorem) under almost every environment for the centered and diffusively scaled walk. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.