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

Autor(es)

Klimek, Aleksander ; Rosati, Tommaso Cornelis

• Tipo de documento: Artigo Científico
• Fonte: ANNALS OF APPLIED PROBABILITY; v. 33, n. 3, p. 67-pg., 2023-06-01.

Resumo

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)

• Processo FAPESP: 15/50122-0 - Fenômenos dinâmicos em redes complexas: fundamentos e aplicações
• Beneficiário: Elbert Einstein Nehrer Macau
• Modalidade de apoio: Auxílio à Pesquisa - Temático