Summary: Department of Mathematics & Statistics
GRADUATE STUDENT SEMINAR
Speaker: Jabib León Sánchez
Title: The self-avoiding walk (SAW) and its conjectured scaling limit in d D 2
Date: April 27, 2007
Time: 10.30 am
Location: College West 307.20
Abstract: The self-avoiding walk (SAW) is a process originally proposed to model poly-
mer chains that have the unique characteristic that no point is visited more than once. It is
important to mention that the main questions about this model remain unsolved rigorously
speaking for dimensions d D 2; 3 and 4.
This seminar will give the necessary tools to understand the procedures and compu-
tations required to state the conjectured scaling limit of a SAW for d = 2 which is the
SchrammLoewner evolution with parameter Ä (SLEÄ) where Ä D 8=3.
Moreover, some notions from complex analysis, a review from stochastic processes
(SRW and Brownian motion), convergence and main elements of the SAW will be pro-
vided. Furthermore, the Loewner equation will be explain in order to obtain the equation
for the stochastic Loewner evolution also called SchrammLoewner evolution.
The seminar will be concluded with the statement of the conjectured scaling limit of
the SAW in two dimensions followed by the results obtained by Tom Kennedy which