## EVENT DETAILS AND ABSTRACT

**The Twenty-Fourth Midwest Probability Colloquium**
**Title:** Scaling limits of two-dimensional statistical physics: Percolation, uniform spanning trees and beyond, I

**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.

**Date:** Friday, October 18, 2002

**Time:** 3:00pm

**Where:** Swift 107

**Contact Person:** Professor Mark Pinsky

**Contact email:** pinsky@math.northwestern.edu

**Contact Phone:** 847-491-5519

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