论文标题
在随机环境中的空间$λ$ -FLEMING-VIOT过程
The spatial $Λ$-Fleming-Viot process in a random environment
论文作者
论文摘要
我们研究了由两种类型组成的人群的大规模行为，这些类型在尺寸d = 1，2中，根据空间lambda-fleming-Viot过程，但受到随机时间独立选择的选择。如果两种类型中的一种与另一种类型相比很少见，我们证明在随机（和奇异）环境中的超棕色运动可以通过超棕色运动来近似。没有稀疏性假设，扩散近似会导致随机电势的Fisher-KPP方程。这些证明是基于安德森·汉密尔顿（Anderson Hamiltonian）的两尺度Schauder估计和半分化近似。
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) environment. 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.
