A NEW LOOK AT DUALITY FOR THE SYMBIOTIC BRANCHING MODEL

• 成果类型: Article
• 署名作者: Hammer, Matthias; Ortgiese, Marcel; Vollering, Florian
• 署名单位: Technical University of Berlin; University of Bath
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1240
• 发表日期: 2018
• 页码: 2800-2862
• 关键词: time behavior; interface; partitions; systems

摘要

The symbiotic branching model is a spatial population model describing the dynamics of two interacting types that can only branch if both types are present. A classical result for the underlying stochastic partial differential equation identifies moments of the solution via a duality to a system of Brownian motions with dynamically changing colors. In this paper, we revisit this duality and give it a new interpretation. This new approach allows us to extend the duality to the limit as the branching rate gamma is sent to infinity. This limit is particularly interesting since it captures the large scale behavior of the system. As an application of the duality, we can explicitly identify the gamma = infinity limit when the driving noises are perfectly negatively correlated. The limit is a system of annihilating Brownian motions with a drift that depends on the initial imbalance between the types.