2019/01/09 by Ninon Fétique, Fétique, Ninon · 1 citation
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1901.02742
arxiv created 2019/01/09 · arxiv updated 2019/01/10
In this paper, we are interested in the speed of convergence of the stochastic billiard evolving in a convex set K. This process can be described as follows: a particle moves at unit speed inside the set K until it hits the boundary, and is randomly reflected, independently of its position and previous velocity. We focus on convex sets in R 2 with a curvature bounded from above and below. We give an explicit coupling for both the continuous-time process and the embedded Markov chain of hitting points on the boundary, which leads to an explicit speed of convergence to equilibrium.