低密度硬球碰撞团簇的基数
On the cardinality of collisional clusters for hard spheres at low density
摘要：
我们恢复调查，开始在arXiv：1408.6571，在气体的$N$硬球的小直径$\varepsilon$的后向集群的统计。后向簇被定义为直接或间接参与给定标记球的时间后向动力学的粒子群。我们得到的平均基数集群的估计相对于平衡措施，全球的时间，均匀的$\varepsilon, N$ $\varepsilon^2 N=1$（玻尔兹曼-格拉德政权）。
英文摘要：
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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