Conformal restriction
- Wendelin Werner (Université de Paris-Sud, Orsay, Laboratoire de Mathématiques, France)
Abstract
We will show an abstract setup that gives another approach to the stochastic Loewner evolution that have been introduced by Oded Schramm, and is closely related to possible scaling limits of planar self-avoiding walks (we will briefly review some basic facts and open questions on self-avoiding walks) as well as other models and to conformal field theory.
More precisely, we will be studying the class of random subsets K of the upper half-plane H, such that the law of K conditioned on K being a subset of A, is exactly the law of f(K) where f is a conformal map from H onto A (if it exists) with f(0)=0 and f(infinity)=infinity. We will in particular see that there exists a unique random simple curve from 0 to infinity satisfying this conformal restriction property.
This is based on joint work with Greg Lawler and Oded Schramm
