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In this article, we obtain the rates of convergence for superdiffusion in theBoltzmann-Grad limit of the periodic Lorentz gas, which is one of thefundamental models to study diffusions in deterministic systems. In theirseminal work, Marklof and Str\"ombergsson proved the Boltzmann-Grad limit ofthe periodic Lorentz gas~\cite{M-Sannals2}, and then Marklof and T\'othestablished a superdiffusive central limit theorem in large time for theBoltzmann-Grad limit~\cite{M-T16}. Based on their work, we apply Stein's methodto derive the convergence rates for the superdiffusion in the Boltzmann-Gradlimit of the periodic Lorentz gas. For the discrete time displacement the rateof convergence in Wasserstein distance is obtained, while in the context of thecontinuous time displacement the result is presented for the Berry-Essen typebound.

The convergence rates for the superdiffusion in the Boltzmann-Grad limit of the periodic Lorentz gas