Extremal regime for one-dimensional Mott variable-range hopping

TL;DR

This paper analyzes the extreme behavior of a one-dimensional Mott random walk under severe blocking, revealing how its position is constrained by environment-dependent barriers with extremal scaling limits.

Contribution

It introduces a novel extremal regime analysis for the Mott random walk, characterizing the limiting behavior of barriers and the walk's distribution between them.

Findings

Barriers have an extremal scaling limit.

The walk's position is confined between environment-measurable barriers.

Distribution of the walk between barriers is asymptotically described.

Abstract

We study the asymptotic behaviour of a version of the one-dimensional Mott random walk in a regime that exhibits severe blocking. We establish that, for any fixed time, the appropriately-rescaled Mott random walk is situated between two environment-measurable barriers, the locations of which are shown to have an extremal scaling limit. Moreover, we give an asymptotic description of the distribution of the Mott random walk between the barriers that contain it.