Random, conformally invariant scaling limits in two dimensions
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Metadata
Formal Metadata
Title  Random, conformally invariant scaling limits in two dimensions 
Title of Series  International Congress of Mathematicians, Madrid 2006 
Number of Parts  33 
Author 
Schramm, Oded

License 
CC Attribution 3.0 Germany: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  10.5446/15974 
Publisher  Instituto de Ciencias Matemáticas (ICMAT) 
Release Date  2006 
Language  English 
Content Metadata
Subject Area  Mathematics 
Abstract  Many mathematical models of statistical physics in two dimensions are either known or conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions of various exponents describing the behavior of these models. Only recently have some of these predictions become accessible to mathematical proof. One of the new developments is the discovery of a oneparameter family of random curves called stochastic Loewner evolution or SLE. The SLE curves appear as limits of interfaces or paths occurring in a variety of statistical physics models as the mesh of the grid on which the model is defined tends to zero. The main purpose of this article is to list a collection of open problems. Some of the open problems indicate aspects of the physics knowledge that have not yet been und erstood mathematically. Other problems are questions about the nature of the SLE curves themselves. Before we present the open problems, the definition of SLE will be motivated and explained, and a brief sketch of recent results will be presented. 
Keywords 
statistical physics conformal invariance stochastic Loewner evolutions percolation 