Markov loops, coverings and fields

TL;DR

This paper explores the connections between Poissonian loop ensembles, their occupation fields, graph coverings, gauge fields, and Eulerian networks, revealing new insights into their interrelations.

Contribution

It introduces novel links between loop ensembles, graph coverings, and gauge fields, advancing understanding of their mathematical interplay.

Findings

Established relationships between Poissonian loop ensembles and Galois coverings.

Connected gauge fields with occupation fields of loop ensembles.

Provided new frameworks for analyzing Eulerian networks.

Abstract

We investigate the relations between the Poissonnian loop ensembles , their occupation fields, non ramified Galois coverings of a graph, the associated gauge fields, and random Eulerian networks.