群体和价格建模：具有吸引力相互作用的跳跃粒子
Modeling Flocks and Prices: Jumping Particles with an Attractive Interaction
摘要：
我们引入并研究了一个新的有限个粒子在实数直线上向前跳跃的模型。跳跃的长度与一切无关，但每个粒子的跳跃率取决于粒子相对于系统质心的相对位置。那些落在后面的粒子的速率较高，而那些在质心前面的粒子的速率较低，提供了一种吸引力的相互作用，使粒子保持在一起。我们证明，在流体的限制，作为粒子的数量趋于无穷大，系统的演化所描述的平均场方程，表现出行波解。还提供了与极值统计的连接。
英文摘要：
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle compared to the center of mass of the system. The rates are higher for those left behind, and lower for those ahead of the center of mass, providing an attractive interaction keeping the particles together. We prove that in the fluid limit, as the number of particles goes to infinity, the evolution of the system is described by a mean field equation that exhibits traveling wave solutions. A connection to extreme value statistics is also provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
