# Equivariant discretizations of diffusions, random walks, and harmonic functions

## TL;DR

This paper explores how to discretize diffusion processes and harmonic functions on covering spaces using Lyons-Sullivan methods, linking continuous and discrete potential theories.

## Contribution

It introduces a framework for equivariant discretizations of diffusions and harmonic functions on covering spaces with group actions.

## Key findings

- Establishes conditions for Lyons-Sullivan discretizations to be equivariant
- Connects continuous diffusion processes with their discrete counterparts
- Provides new insights into the function theory on covering spaces

## Abstract

For covering spaces and properly discontinuous actions with compatible diffusion processes, we discuss Lyons-Sullivan discretizations of the processes and the associated function theory.