Discrete Approximation of Symmetric Jump Processes on Metric Measure Spaces

TL;DR

This paper establishes criteria for the convergence of discrete Markov chains to symmetric jump processes on metric measure spaces and explores their applications, including scaling limits of random walks in random conductance environments.

Contribution

It provides general criteria for tightness and weak convergence of discrete Markov chains to symmetric jump processes, extending approximation methods on metric measure spaces.

Findings

Criteria for tightness and weak convergence established

Application to discrete approximation of symmetric jump processes

Insights into scaling limits of random walks in random conductance

Abstract

In this paper we give general criteria on tightness and weak convergence of discrete Markov chains to symmetric jump processes on metric measure spaces under mild conditions. As an application, we investigate discrete approximation for a large class of symmetric jump processes. We also discuss some application of our results to the scaling limit of random walk in random conductance.