Back to Boundaries in Billiards

TL;DR

This paper establishes Poisson limit laws for open billiard systems with boundary holes, covering various billiard types and emphasizing applications in physical systems.

Contribution

It introduces the first proof of Poisson limit laws for boundary holes in diverse billiard models, extending previous phase space hole results.

Findings

Poisson limit laws hold for boundary holes in Sinai billiards

Results apply to diamond and semi-dispersing billiards

Includes billiards with slow decay of correlations

Abstract

We prove Poisson limit laws for open billiards where the holes are on the boundaries of billiard tables (rather than some abstract holes in the phase space of a billiard). Such holes are of the main interest for billiard systems, especially for applications. Sinai billiards with or without a finite horizon, diamond billiards, and semi-dispersing billiards, as well as focusing billiards with slow decay of correlations, are considered.