INFINITE RATE MUTUALLY CATALYTIC BRANCHING IN INFINITELY MANY COLONIES: THE LONGTIME BEHAVIOR

• 成果类型: Article
• 署名作者: Klenke, Achim; Mytnik, Leonid
• 署名单位: Johannes Gutenberg University of Mainz; Technion Israel Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP621
• 发表日期: 2012
• 页码: 103-129
• 关键词: ergodic-theorems; MODEL; systems

摘要

Consider the infinite rate mutually catalytic branching process (IMUB) constructed in [Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence (2008) Preprint] and [Ann. Probab. 38 (2010) 479-497]. For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent. On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.