标题： 稀释硬球气体动力学的簇展开 显示英文标题

标题： Cluster expansion for a dilute hard sphere gas dynamics

摘要： 在[7]中，开发了一种聚类展开方法，用于研究硬球动力学在玻尔兹曼方程周围的涨落。这种方法提供了对经验测度的指数矩的精确控制，从而推导出了随机玻尔兹曼方程和大偏差估计。[7]中的聚类展开是在BBGKY层次结构的层面上实现的，这是研究确定性动力学的标准工具[11]。在本文中，我们引入了一种替代方法，其中聚类展开直接应用于粒子系统的实际轨迹。这为在低密度极限下研究硬球动力学提供了一个新的视角，使得能够恢复[7]中获得的结果，并且还可以描述粒子轨迹的实际聚类情况。 显示英文摘要

摘要： In [7], a cluster expansion method has been developed to study the fluctuations of the hard sphere dynamics around the Boltzmann equation. This method provides a precise control on the exponential moments of the empirical measure, from which the fluctuating Boltzmann equation and large deviation estimates have been deduced. The cluster expansion in [7] was implemented at the level of the BBGKY hierarchy, which is a standard tool to investigate the deterministic dynamics [11]. In this paper, we introduce an alternative approach, in which the cluster expansion is applied directly on real trajectories of the particle system. This offers a fresh perspective on the study of the hard sphere dynamics in the low density limit, allowing to recover the results obtained in [7], and also to describe the actual clustering of particle trajectories.