Dynamical random walk on the integers with a drift

TL;DR

This paper investigates dynamical random walks on integers with internal states driven by expanding maps, establishing conditions under which the particle's position follows the Central Limit Theorem, thus linking dynamical systems and probabilistic limit laws.

Contribution

It introduces a framework for dynamical random walks with internal states and provides conditions ensuring CLT behavior for the particle's position.

Findings

Conditions for CLT in dynamical random walks with expanding maps

Link between dynamical systems and probabilistic limit theorems

Framework for analyzing internal state-driven random walks

Abstract

In this note we study dynamical random walks (DRW) with internal states. We consider a particle which performs a dynamical random walk on $\mathbb{Z}$ and whose local dynamics is given by expanding maps. We provide sufficient conditions for the position of the particle $z_n$ to satisfy the Central Limit Theorem.