The spatial Λ-Fleming–Viot process in a random environment

The spatial Λ-Fleming–Viot process in a random environment

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 appr...

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Bibliographic Details
Published in:The Annals of applied probability Vol. 33; no. 3; p. 2426
Main Authors: Klimek, Aleksander, Rosati, Tommaso Cornelis
Format: Journal Article
Language:English
Published: Hayward Institute of Mathematical Statistics 01-06-2023
Subjects:
Approximation
Brownian motion
Random variables
Spatial analysis
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Summary: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.
ISSN:1050-5164
2168-8737
DOI:10.1214/22-AAP1871