A new equidistribution theorem on parameter space with applications to statistical physics

Roland Roeder

I will explain two interesting problems from statistical physics which are presently too hard to understand for the classical Z^d lattices for d > 1. In the case of hierarchical lattices, they can be studied using the Migdal-Kadanoff renormalization. This motivates a rather general theorem on the equidistribution of parameter values for algebraic families of rational maps. A key technique in the proof is a theorem on arithmetic dynamics due to Silverman. The results in this talk were motivated by many interesting conversations with Robert Shrock and the equidistribution theorem is joint with Ivan Chio.

http://scgp.stonybrook.edu/video_portal/video.php?id=4494

Simons- Program: Renormalization and universality in Conformal Geometry, Dynamics, Random Processes, and Field Theory