THE SPATIAL A-FLEMING-VIOT PROCESS IN A RANDOM ENVIRONMENT

• 成果类型: Article
• 署名作者: Klimek, Aleksander; Rosati, Tommaso Cornelis
• 署名单位: University of Edinburgh; University of Warwick
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1871
• 发表日期: 2023
• 页码: 2426-2492
• 关键词: species richness; Heterogeneity; MODEL

摘要

We study the large scale behaviour of a population consisting of two types which evolve in dimension d = 1, 2 according to a spatial Lambda-Fleming-Viot process subject to random time-independent selection. If one of the two types is rare compared to the other, we prove that its evolution can be approximated by a super-Brownian motion in a random (and singular) en-vironment. Without the sparsity assumption, a diffusion approximation leads to a Fisher-KPP equation in a random potential. The proofs build on two -scale Schauder estimates and semidiscrete approximations of the Anderson Hamiltonian.