论文标题
具有平均场相互作用的粒子系统的大规模行为：行驶波解决方案
Large-scale behavior of a particle system with mean-field interaction: Traveling wave solutions
论文作者
论文摘要
我们使用概率方法来研究平均场模型的性质，这是某些具有平均场相互作用的粒子系统的大规模限制。底层粒子系统使$ n $颗粒在实际线路上向前移动。具体而言，每个粒子在某些时间点上“向前跳”，而瞬时速度速率是由于粒子位置的整体分布中粒子位置分位数的降低功能给出的。当$ n $大时，一个平均场模型描述了粒子分布的演变。从本质上讲，它是对特定类中的截面方程式的解决方案。我们的主要结果涉及在跳跃率函数和跳跃大小分布的一般条件下，在流动波和均值的平均场模型的存在和独特性。
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.
