Multiple scale analysis of clusters in spatial branching models

• 成果类型: Article
• 署名作者: Klenke, A
• 署名单位: University of Erlangen Nuremberg
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1023481107
• 发表日期: 1997
• 页码: 1670-1711
• 关键词: hierarchically interacting diffusions; particle-systems; voter model; time; persistence; dimensions

摘要

In this paper we will investigate the long time behavior of critical branching Brownian motion and (finite variance) super-Brownian motion (the so-called Dawson-Watanabe process) on R-d. These processes are known to be persistent if d greater than or equal to 3; that is, there exist nontrivial equilibrium measures. If d less than or equal to 2, they cluster; that is, the processes converge to the 0 configuration while the surviving mass piles up in so-called clusters. We study the spatial profile of the clusters in the critical dimension d = 2 via multiple space scale analysis. We will also investigate the long-time behavior of these models restricted to finite boxes in d greater than or equal to 2. On the way, we develop coupling and comparison methods for spatial branching models.