3 papers
math.PR2018
Billiards with Markovian reflection laws
Clayton Barnes, Krzysztof Burdzy, Carl-Erik Gauthier
We construct a class of reflection laws for billiard processes in the unit interval whose stationary distribution for the billiard position and its velocity is the product of the u…
math.PR2018
Knudsen gas in flat tire
Krzysztof Burdzy, Carl-Erik Gauthier
We consider random reflections (according to the Lambertian distribution) of a light ray in a thin variable width (but almost circular) tube. As the width of the tube goes to zero,…
math.PR2017
Central Limit Theorem for a Self-Repelling Diffusion
Carl-Erik Gauthier
We prove a Central Limit Theorem for the finite dimensional distributions of the displacement for the 1D self-repelling diffusion which solves \begin{equation*} dX_t =dB_t -\big(G'…