## Probability Seminar: Gourab Ray

- Date: 11/21/2018
- Time: 16:00

Lecturer(s):
Gourab Ray, University of Victoria

Location:

University of British Columbia

Topic:

Logarithmic variance for uniform homomorphisms on Z^2

Description:

Take the n by n box in the square lattice and fill it with integers where the integers on adjacent vertices only differ by +1 or -1. How large can a typical value be?

We prove that the variance at a point blows up like log n which in particular implies that such a function is delocalized. This is a consequence of a Russo Seymour Welsh theory that we build for such functions. I will also discuss a connection with the six-vertex model (also called the square ice model).

Joint work with **Hugo Duminil Copin, Matan Harel, Benoit Laslier and Aran Raoufi.**

Other Information:

Location: ESB 2012