A limit result for a system of particles in random environment

TL;DR

This paper studies an infinite one-dimensional particle system where each particle performs Sinai's random walk in a random environment, demonstrating that particles tend to cluster near specific lattice points depending on the environment, time, and initial positions.

Contribution

It establishes a probabilistic limit result showing particles are localized near certain lattice points in a Sinai's walk system in a random environment.

Findings

Particles are trapped near well-defined lattice points at large times.

The trapping points depend on the environment, initial positions, and time.

The result provides insight into localization phenomena in random environments.

Abstract

We consider an infinite system of particles in one dimension, each particle performs independant Sinai's random walk in random environment. Considering an instant $t$, large enough, we prove a result in probability showing that the particles are trapped in the neighborhood of well defined points of the lattice depending on the random environment the time $t$ and the starting point of the particles.