ON THE COMING DOWN FROM INFINITY OF COALESCING BROWNIAN MOTIONS

• 成果类型: Article
• 署名作者: Barnes, Clayton; Mytnik, Leonid; Sun, Zhenyao
• 署名单位: Technion Israel Institute of Technology; Beijing Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1640
• 发表日期: 2024
• 页码: 67-92
• 关键词: partial-differential equations; stochastic pdes; heat-equation; particles; Duality

摘要

Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are infinitely many initial particles in the system. We give a necessary and sufficient condition for the number of particles to come down from infinity. We also identify the rate of this coming down from infinity for different initial configurations.