The spatial $\Lambda$-Fleming-Viot process in a random environment
Probability
2021-11-30 v2
Abstract
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.
Cite
@article{arxiv.2004.05931,
title = {The spatial $\Lambda$-Fleming-Viot process in a random environment},
author = {Aleksander Klimek and Tommaso Cornelis Rosati},
journal= {arXiv preprint arXiv:2004.05931},
year = {2021}
}