Thursday, December 1, 2022, 3:30 – 4:30pm

The Potts model is a distribution on q-colorings of a graph, used to represent spin configurations of a system of particles. Intuitively we expect most configurations to be "solid-like" at low temperatures and "gas-like" at high temperatures. We prove a precise version of this statement for d-regular edge-expanding graphs. We also consider the question of whether or not there are efficient algorithms for approximate counting and sampling from the model, and show that such algorithms exist at almost all temperatures. In this talk, I will introduce the different tools we use in our proofs, which come from both statistical physics (polymer models, cluster expansion) and combinatorics (a new container-like result, Karger's randomized min-cut algorithm).

This is joint work with Charlie Carlson, Ewan Davies, Nicolas Fraiman, Alexandra Kolla, and Aditya Potukuchi.

Event Type: Seminars
Room Number: In Person
Building: Wean Hall 8220
Speaker's Name: CORRINE YAP
Speaker Website: sites.math.rutgers.edu…
Speaker's Professional Title: Ph.D. Student, Department of Mathematics - Hill Center, Rutgers University
Talk Title: Algorithms for the Potts model on expander graphs
Affiliations: Computer Science Department (CSD)
Organization(s): Department of Mathematical Sciences
Event Website Title: Series Website
Event Website URL: www.cmu.edu…