Self-avoiding walk in dimension 4

Non-equilibrium Dynamics and Random Matrices
Topic:Self-avoiding walk in dimension 4
Speaker:Roland Bauerschmidt
Affiliation:Member, School of Mathematics
Date:Tuesday, January 28
Time/Room:2:00pm - 3:00pm/S-101
Video Link:https://video.ias.edu/nedrm/2014/0128-RolandBauerschmidt

The (weakly) self-avoiding walk is a basic model of paths on the d-dimensional integer lattice that do not intersect (have few intersections), of interest from several different perspectives. I will discuss a proof that, in dimension 4, the susceptibility of the weakly self-avoiding walk diverges with an explicit logarithmic correction as the critical point is approached. The argument is based on a representation of the weakly self-avoiding walk as a supersymmetric field theory which is studied with a renormalization group method. This is joint work with Brydges and Slade.