Randomly trapped random walks

TL;DR

This paper introduces a general trapping model for random walks on graphs, characterizes their scaling limits on , and identifies conditions for convergence to various well-known and new stochastic processes.

Contribution

It proposes a unified framework for trapping in random walks and classifies their scaling limits, including new classes like spatially subordinated Brownian motions.

Findings

Identifies conditions for convergence to fractional kinetics and singular diffusion.

Introduces a new class called spatially subordinated Brownian motions.

Provides examples illustrating the theoretical results.

Abstract

We introduce a general model of trapping for random walks on graphs. We give the possible scaling limits of these Randomly Trapped Random Walks on $\mathbb {Z}$. These scaling limits include the well-known fractional kinetics process, the Fontes-Isopi-Newman singular diffusion as well as a new broad class we call spatially subordinated Brownian motions. We give sufficient conditions for convergence and illustrate these on two important examples.