Erwin Bolthausen (University of Zurich)

One-dimensional models with Kac type interactions, and their connection with the polaron problem.

A long standing open problem in mathematical physics is the determination of the effective mass of the Frohlich polaron in the strong coupling limit. The problem can be formulated in terms of a three dimensional Brownian motion with an attractive Kac type interaction. The strong coupling corresponds to a small Kac parameter. There is a heuristic derivation by Spohn which is generally considered to give the correct asymptotics, but a proof is still lacking. We will discuss the Spohn picture, discuss some recent progress, and present a simplified model with the same basic structure, for which the conjecture can be proved.