Markov paths, loops and fields

TL;DR

This paper explores the relationships between Markov loop occupation fields and free fields, providing insights into their mathematical connections through an extended lecture series.

Contribution

It introduces new theoretical links between Markov loop occupation fields and free fields, expanding understanding of their interplay.

Findings

Established mathematical relations between Markov loops and free fields

Extended previous lecture series with new theoretical insights

Enhanced understanding of occupation fields in Markov processes

Abstract

This is an extended version of a series of lectures given in St Flour. It includes a discussion of relations between the occupation field of Markov loops with the corresponding free field.