# A note on the finite-dimensional distributions of dispersing billiard processes

## TL;DR

This paper establishes a correlation bound for dispersing billiard processes with random initial conditions, enabling the derivation of limit theorems and aiding the study of more general functionals.

## Contribution

It introduces a functional correlation bound for finite-dimensional distributions of dispersing billiards, facilitating analysis of their limit behaviors.

## Key findings

- Correlation bound implies several limit theorems
- Tool for studying general functionals of billiard processes
- Enhances understanding of dispersing billiard dynamics

## Abstract

In this short note we consider the finite-dimensional distributions of sets of states generated by dispersing billiards with a random initial condition. We establish a functional correlation bound on the distance between the finite-dimensional distributions and corresponding product distributions. We demonstrate the usefulness of the bound by showing that it implies several limit theorems. The purpose of this note is to provide a tool facilitating the study of more general functionals of the billiard process.