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Department of Mathematics & Statistics GRADUATE STUDENT SEMINAR

Summary: Department of Mathematics & Statistics
Speaker: Luis Diego León Chi
Title: Scaling limit of loop-erased random walk in d D 2
Date: April 27, 2007
Time: 9.30 am
Location: College West 307.20
Abstract: The loop-erased random walk (LERW) was first studied in 1980 by Lawler
as an attempt to analyze the self-avoiding walk (SAW), which provides a model for a
polymer molecule with excluded volume. The self-avoiding walk is simply a path on a
lattice that does not visit the same site more than once. Proving things about the collection
of all such paths is a formidable challenge to rigorous mathematical methods. Eventually,
it was discovered that SAW and LERW are in different universality classes.
LERW existed as an interesting mathematical idea without any applicability until
1996, when Wilson discovered its use in finding spanning trees of graphs in an efficient
way. This model has continued to receive attention in recent years, in part because of
connections with uniform spanning trees (UST).
In 1999, Schramm introduced this one-parameter family of random growth processes
based on Loewner's differentialequation. This process is called the stochastic (or Schramm­
Loewner) evolution SLEÄ where the parameter Ä is the time scaling constant for the driv-


Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina


Collections: Mathematics