Lorentz Process with shrinking holes in a wall

Abstract

We ascertain the diffusively scaled limit of a periodic Lorentz process in a strip with an almost reflecting wall at the origin. Here, almost reflecting means that the wall contains a small hole waning in time. The limiting process is a quasi-reflected Brownian motion, which is Markovian but not strong Markovian. Local time results for the periodic Lorentz process, having independent interest, are also found and used.

References in corpus (1)

• Motion in a Random Force Field

Cited by in corpus (4)

• Leaking Chaotic Systems
• Non equilibrium density profiles in Lorentz tubes with thermostated boundaries
• On a Brownian motion with a hard membrane
• Escape dynamics through a continuously growing leak