Markov loops topology

TL;DR

This paper investigates the topological properties of Markov loop ensembles, extending the understanding of their structure within the context of Markov processes and graph-based Markov chains.

Contribution

It provides a novel exploration of the topological aspects of Markov loop ensembles, building on prior work on loop soups and Markov processes.

Findings

Topological properties of Markov loop ensembles are characterized.

Connections between loop ensembles and graph topology are established.

Framework for analyzing loop structures in Markov chains is developed.

Abstract

Since the work of Lawler and Werner on "loop soups", these ensembles have also been the object of many investigations. Their properties can be studied in the context of rather general Markov processes, in particular Markov chains on graphs. The purpose of the present work is to explore their topological properties.