The Fröhlich polaron describes the slow movement of an electron in a polar crystal. A long open problem is the asymptotics of the effective mass of the polaron in the strong coupling limit. An application of the Feynman-Kac formula leads to Brownian motion perturbed by a pair potential. The point process representation introduced by Mukherjee and Varadhan represents this path measure as a mixture of Gaussian measures, the respective mixing measure can be interpreted in terms of a perturbed birth and death process. I will present joint work with Volker Betz in which we apply this representation in order to give a first quantitative lower bound on the effective mass. I will additionally show how the renewal structure of the underlying point processes can be applied in order to study the whole energy-momentum relation. 

https://indico.math.cnrs.fr/event/8609/