# Velocity estimates for symmetric random walks at low ballistic disorder

## TL;DR

This paper provides asymptotic estimates for the velocity of symmetric random walks with small local drifts in random environments, extending previous theoretical results and expansions.

## Contribution

It introduces new asymptotic estimates for the velocity of perturbed symmetric random walks, complementing and extending prior theoretical work.

## Key findings

- Derived asymptotic velocity estimates for low-disorder random walks
- Extended theoretical understanding of random walk behavior in perturbed environments
- Complemented previous results with new expansion techniques

## Abstract

We derive asymptotic estimates for the velocity of random walks in random environments which are perturbations of the simple symmetric random walk but have a small local drift in a given direction. Our estimates complement previous results presented by Sznitman and are in the spirit of expansions obtained by Sabot.