Tel Aviv University Dear all, 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 Time: 14:30 Place: Schreiber 309 Abstract: 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. Best regards, Ron Seminar webpage: <http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Ron Peled <peledron@gmail.com>