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

Author(s)

Klimek, Aleksander ; Rosati, Tommaso Cornelis

• Document type: Journal article
• Source: ANNALS OF APPLIED PROBABILITY; v. 33, n. 3, p. 67-pg., 2023-06-01.

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) 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. (AU)

• FAPESP's process: 15/50122-0 - Dynamic phenomena in complex networks: basics and applications
• Grantee: Elbert Einstein Nehrer Macau
• Support Opportunities: Research Projects - Thematic Grants