Title:
A brownian limit perturbed by a microscopic potential.

Abstract:
This is a joint work with Jeremy Clark. I will discuss a  
one-dimensional model for a massive particle interacting with a gas of  
light particles and under the influence of a microscopic periodic  
potential. Our model is Markovian and is given by a linear Boltzmann  
equation. We study the behavior of the momentum of the massive  
particle as the ratio of a single reservoir particle to the massive  
particle tends to zero. For the usual scaling, the microscopic  
potential does not appear in the Brownian limit, and the momentum  
converges to the Orstein-Uhlenbeck process. However, for a smaller  
scaling, the total drift in momentum converges to a Brownian motion  
time-changed by the local time of the Orstein-Uhlenbeck process.