MIT Probability Seminar

Monday, February 05, 2024 at 4:15pm to 5:15pm

Building 2
182 MEMORIAL DR, Cambridge, MA 02139

Speaker: Matan Harel (Northeastern University)

Title: The loop O(n) model and the XOR trick


The loop O(n) model is a model for random configurations of non-overlapping loops on the hexagonal lattice, which contains many models of interest (such as the Ising model, self-avoiding walks, and random Lipshitz functions) as special cases. Its conjectured phase diagram is very rich, and the model is believed to undergo several different phase transitions. Over the last decade, several features of the phase diagram have been proven rigorously, mostly through the use of particular bijections or observables at critical values. We use an expansion around critical percolation to prove that, near the values that correspond to critical Bernoulli percolation, the loop O(n) model has long , infinitely-nested loops, without relying on exact solvability. This is joint work with Nick Crawford, Alexander Glazman, and Ron Peled.

Event Type


Events By Audience

Public, MIT Community, Students, Alumni, Faculty, Staff

Events By School

School of Science


Seminar, MIT, MITMath


Department of Mathematics
Add to my calendar

Recent Activity