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Bibliographic Details
Main Authors: Matthies, Karsten, Syntaka, Theodora
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2405.04449
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Table of Contents:
  • We will revisit the classical questions of understanding the statistics of various deterministic dynamics of $N$ hard spheres of diameter $\varepsilon$ with random initial data in the Boltzmann-Grad scaling as $\varepsilon$ tends to zero and $N$ tends to infinity. The convergence of the empiric particle dynamics to the Boltzmann-type dynamics is shown using semigroup methods to describe probability measures on collision trees associated to physical trajectories in the case of a Rayleigh gas. As an application we derive the diffusion equation by a further rescaling.