Vortrag von 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)