EVENT DETAILS AND ABSTRACT

Title: Scaling limits of two-dimensional statistical physics: Percolation, uniform spanning trees and beyond, II
Speaker: Oded Schramm
Speaker Info: Microsoft
Brief Description:
Special Note:
Abstract:

Many random processes on lattices in two dimensions are believed to have conformally invariant limits as the mesh refines. The classical example is simple random walk, which converges to Brownian motion. In the last two years, this has also been proved (by several authors) for critical percolation on the triangular grid, for loop-erased random walk, and for uniform spanning trees. All these scaling limits can be described using a single one-parameter family of random paths called SLE. There are several conjectures relating SLE to the self-avoiding walk and to interfaces of the random cluster measures, as well as several other studied statistical physics processes. Our goals will be to give a survey of the current state of knowledge, to explain some of the basic ideas, and to describe conjectures and open problems.