Kramers-Fokker-Planck equation with a short-range potential

In this talk we introduce the Kramers-Fokker-Planck equation as a way to describe Brownian motion. The summary of known results about the corresponding operator is presented and then our main aim is to study large-time asymptotics of solutions of the KFP equation with a short-range potential in dimension one. After finding the expansion of the resolvent near the threshold of the essential spectrum we may employ representation formula of the semigroup in terms of the resolvent to obtain the asymptotics of solutions.