Topics in loop measures and the loop-erased walk

TL;DR

This paper discusses key ideas and recent results related to loop measures and the loop-erased random walk, based on a course taught at the University of Chicago.

Contribution

It provides a personal selection of important concepts and recent findings in the study of loop measures and loop-erased walks.

Findings

Summarizes recent results in loop measures and loop-erased walks.

Highlights key ideas from a course on the topic.

Provides insights into the mathematical structure of these processes.

Abstract

These are notes based on a course that I gave at the University of Chicago in Fall 2016 on "Loop measures and the loop-erased random walk." This is not intended to be a comprehensive view but rather a personal selection of some key ideas including some recent results.