- Sponsor
- Department of Mathematics
- Speaker
- Jaya Manthripragada
- Contact
- Rui Yu
- ruiyu6@illinois.edu
- Views
- 7
- Originating Calendar
- Mathematics Seminar Series: Probability
Title: Introduction to Loop Measures II: Loop-Erased Random Walks and Spanning Trees
Abstract: In the previous talk, we introduced rooted and unrooted loop measures, their generating functions, and loop soups. In this talk, we will explore the connection between loop measures and spanning trees through loop-erased random walks. We will first introduce chronological loop erasure and derive a formula for the weights of loop-erased paths in terms of loop measures. We will then discuss Wilson's algorithm for generating spanning trees and show how it produces a uniform spanning tree on a finite connected graph.
Reference: Lawler, G. F., & Limic, V. (2010). Random Walk: A Modern Introduction, Sections 9.5 and 9.7. Cambridge University Press.