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arXiv · 2005.09962

On the cardinality of collisional clusters for hard spheres at low density

Mario Pulvirenti·Sergio Simonella
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Abstract

We resume the investigation, started in arXiv:1408.6571, of the statistics of backward clusters in a gas of $N$ hard spheres of small diameter $\varepsilon$. A backward cluster is defined as the group of particles involved directly or indirectly in the backwards-in-time dynamics of a given tagged sphere. We obtain an estimate of the average cardinality of clusters with respect to the equilibrium measure, global in time, uniform in $\varepsilon, N$ for $\varepsilon^2 N=1$ (Boltzmann-Grad regime).

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Mario Pulvirenti, Sergio Simonella. 2020-05-20. On the cardinality of collisional clusters for hard spheres at low density. https://arxiv.org/abs/2005.09962

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