A Note on Transportation Cost Inequalities for Diffusions with Reflections

TL;DR

This paper establishes dimension-free transportation cost inequalities for reflected Brownian motions and related diffusions, including models with rank-based interactions, improving upon previous dimension-dependent results.

Contribution

It proves a dimension-free transportation cost inequality for reflected diffusions and extends it to rank-based particle systems like the infinite Atlas model.

Findings

Dimension-free transportation inequalities for reflected Brownian motions.

Extension to diffusions with rank-based drifts and diffusions.

Application to infinite Atlas model with improved bounds.

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.