Konferenz: Workshop on the occasion of Erwin Bolthausen's 70th birthday


The mean-field Polaron model

{{_Ltalk:R}} Prof. Dr. Wolfgang König
Datum: 15.09.16   Zeit: 11.00 - 11.50   Raum: Y16G05

We consider mean-field interactions corresponding to Gibbs measures on Brownian paths in three dimensions. The interaction is self-attractive and is given by a singular Coulomb potential. The logarithmic asymptotics of the partition function were identified in the 1980s by Donsker and Varadhan in terms of the Pekar variational formula. In this talk, we analyse the mean-field path measures; in particular, we give a proof of the convergence of the normalized occupation measures towards an explicit mixture of the maximizers of the Pekar variational problem. The starting point is a compactification procedure recently developed by Mukherjee and Varadhan.

(joint work with E. Bolthausen and C. Mukherjee)