A Note on Transportation Cost Inequalities for Diffusions with Reflections

Abstract

We prove that reflected Brownian motion with normal reflections in a convex domain satisfies a dimension free Talagrand type transportation cost-information inequality. The result is generalized to other reflected diffusions with suitable drifts and diffusions. We apply this to get such an inequality for interacting Brownian particles with rank-based drift and diffusion coefficients such as the infinite Atlas model. This is an improvement over earlier dimension-dependent results.

10 pages. Keywords: Reflected Brownian motion, Wasserstein distance, relative entropy, transportation cost-information inequality, concentration of measure, competing Brownian particles