## 2009 Probability Seminar - 07

- Date: 03/18/2009

University of British Columbia

Using multiple SLE to explain a certain observable in the 2d Ising model

The Schramm-Loewner evolution (SLE) is a one-parameter family of random

growth processes that has been successfully used to analyze a number of

models from two-dimensional statistical mechanics. Currently there is

interest in trying to formalize our understanding of conformal field

theory using SLE. Smirnov recently showed that the scaling limit of

interfaces of the 2d critical Ising model can be described by SLE(3).

The primary goal of this talk is to explain how a certain non-local

observable of the 2d critical Ising model studied by Arguin and

Saint-Aubin can be rigorously described using multiple SLE(3) and

Smirnov's result. As an extension of this result, we explain how to

compute the probability that a Brownian excursion and an SLE(k) curve,

0<4, do not intersect.

3:00pm-4:00pm, WMAX 216