Diffusive Decay of the Environment Viewed by the Particle

TL;DR

This paper establishes an optimal diffusive decay rate for the environment viewed by a particle in a random walk with independent conductances, assuming finite second moments, using a concise analytic proof.

Contribution

It provides a short, elementary proof of the optimal diffusive decay in a random walk environment with finite second moments of conductances.

Findings

Proves optimal diffusive decay rate for environment viewed by particle

Uses analytic approach of Gloria, Neukamm, and Otto

Assumes finite second moment of conductances

Abstract

We prove an optimal diffusive decay of the environment viewed by the particle in random walk among random independent conductances, with, as a main assumption, finite second moment of the conductance. Our proof, using the analytic approach of Gloria, Neukamm and Otto, is very short and elementary.