Deriving crystallizing probability model from classical mechanics

把重粒子(S)置于理想气体环境中，一个系统由无限多个具有一定初始分布的轻粒子组成，并假设粒子之间的相互作用是非随机的。我们对重粒子(S)在轻粒子质量收敛到0时的极限行为感兴趣。当恰好存在两个不同类型的重粒子时，我们证明了所考虑的随机过程的分布收敛于有反射的扩散；对于两个重粒子类型相同且具有相对效率的情况，我们通过证明相应的随机微分方程的收敛，得到了候选极限过程的具体表达式。对于具有一个重粒子的一维情形，也研究了与波动环境类似的问题。

Put heavy particle(s) into an ideal gas environment, a system consists of infinitely many light particles with a certain initial distribution, and assume that the interactions between particles are non-random. We are interested in the problem of the limit behavior of the heavy particle(s) when the mass of the light particles converges to 0. When there are exact two heavy particles of different types, we proved that the distribution of the considered stochastic process converges to a diffusion with reflecting; for the case where the two heavy particles are of same type with relative efficiency, we found the concrete expression of the candidate limit process by proving the convergence of the corresponding stochastic differential equation. The similar problem with wave environment is also studied for the case with one heavy particle and in one-dimension.