Some challenges in the theory of (semi)-dispersing billiards (original) (raw)

The paper explores challenges in the theory of (semi)-dispersing billiards, particularly in understanding correlation decay in higher dimensions, a significant problem in the field. It discusses the Boltzmann-Sinai ergodic hypothesis and recent results that rely on complexity conditions essential for proving ergodicity in dispersing billiards. An introduction to the Penrose-Lorentz process and its implications for diffusive behavior is also provided, setting the stage for future research directions.