Tel Aviv University
This week at the Horowitz seminar on Probability, Ergodic Theory and
Dynamical Systems at Tel Aviv University we are happy to have:
Speaker: Ariel Yadin, Ben-Gurion University
Title: Super-critical self avoiding walk is space filling
Date: Monday, November 21
Place: Schreiber 309
The Self Avoiding Walk (SAW) is a model proposed by Flory in the 50's
to study polymer chains. The models studied basically refer to
choosing a self avoiding path, P, in a lattice, with probability
proportional to x^|P| , where |P| is the length of P. Here x is some
positive real parameter. There is a conjectured phase transition of
the behavior of a typical path according to whether x is above or
below the "connective constant" of the lattice. The sub-critical case
has been studied by Ioffe.
In dimension 2, it is conjectured that the critical case should
converge to SLE(8/3). Resolving this conjecture is a major open
problem in probability. In fact not much is known about geometric
properties of the 2D SAW. The super-critical SAW is expected to be
space-filling, and in dimension 2 to have the scaling limit SLE(8),
which is a space filling curve.
In joint work with Gady Kozma and Hugo Duminil-Copin we show that
super-critical SAW is space filling. The proof is fairly natural and
uses a renormalization idea. The proof works for different lattices
and all dimensions > 1.
We will not assume prior knowledge of SAW or SLE.
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel <firstname.lastname@example.org>
Announcement from: Ron Peled <email@example.com>