具有平均场相互作用的粒子系统的大尺度行为：行波解
Large-scale behavior of a particle system with mean-field interaction: Traveling wave solutions
摘要：
我们使用概率的方法来研究平均场模型的性质，所产生的大规模限制的某些粒子系统的平均场相互作用。基础粒子系统是这样的，即$n$粒子在实数线上向前移动。具体地，每个粒子在某些时间点“向前跳跃”，其中跳跃的瞬时速率由粒子位置的总体分布内的粒子位置分位数的减函数给出。当$n$较大时，平均场模型描述了粒子分布的演化。它本质上是一个解决方案的积分微分方程在一定的类。我们的主要结果关注的存在性和唯一性-和吸引力-平均场模型，这是行波，在一般条件下的跳跃率函数和跳跃大小分布。
英文摘要：
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real line. Specifically, each particle "jumps forward" at some time points, with the instantaneous rate of jumps given by a decreasing function of the particle's location quantile within the overall distribution of particle locations. A mean-field model describes the evolution of the particles' distribution, when $n$ is large. It is essentially a solution to an integro-differential equation within a certain class. Our main results concern the existence and uniqueness of -- and attraction to -- mean-field models which are traveling waves, under general conditions on the jump-rate function and the jump-size distribution.
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