Random Walk in Random Environment: A short introduction

TL;DR

This paper introduces the concept of Random Walk in a Random Environment (RWRE), explaining key ideas like recurrence and potential, and explores its application to graphene conduction with an electrical perspective.

Contribution

It provides an accessible introduction to RWRE, combining intuitive explanations with an electrical analogy and demonstrating its relevance to graphene conduction.

Findings

Electrical analogy offers new insights into RWRE behavior

Application to graphene conduction illustrates practical relevance

Enhanced understanding of recurrence and potential in RWRE

Abstract

This is a report of a scientific project carried out at Ecole Centrale Casablanca in 2019. This work is an entry into the world of Random Walk in a Random Environment (RWRE). We will discuss some intuitive concepts such as recurrence, location, and random potential. We will thereafter focus on providing an "electrical" understanding of this type of walk and finally explore an application of RWRE to graphene conduction.