2021/08/22 by Songzi Li, Li, Songzi
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2108.09773
openalex publication_date 2021/08/22 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this article, we obtain the rates of convergence for superdiffusion in the Boltzmann-Grad limit of the periodic Lorentz gas, which is one of the fundamental models to study diffusions in deterministic systems. In their seminal work, Marklof and Strömbergsson proved the Boltzmann-Grad limit of the periodic Lorentz gas~\citeM-Sannals2, and then Marklof and Tóth established a superdiffusive central limit theorem in large time for the Boltzmann-Grad limit~\citeM-T16. Based on their work, we apply Stein's method to derive the convergence rates for the superdiffusion in the Boltzmann-Grad limit of the periodic Lorentz gas. For the discrete time displacement the rate of convergence in Wasserstein distance is obtained, while in the context of the continuous time displacement the result is presented for the Berry-Essen type bound.