From flows of Lambda Fleming-Viot processes to lookdown processes via flows of partitions

Abstract

The goal of this paper is to unify the lookdown representation and the stochastic flow of bridges, which are two approaches to construct the $\Lambda$-Fleming-Viot process along with its genealogy. First we introduce the stochastic flow of partitions and show that it provides a new formulation of the lookdown representation. Second we study the asymptotic behaviour of the $\Lambda$-Fleming-Viot process and we provide sufficient conditions for the existence of an infinite sequence of Eves that generalise the primitive Eve of Bertoin and Le Gall. Finally under the condition that this infinite sequence of Eves does exist, we construct the lookdown representation pathwise from a flow of bridges.

49 pages, 1 figure. v4: proof of the measurability of the Eves added, additional details at several places

References in corpus (7)

• A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks
• On the Eve property for CSBP
• Kingman's coalescent and Brownian motion
• From flows of Lambda Fleming-Viot processes to lookdown processes via flows of partitions
• Generalized Fleming-Viot processes with immigration via stochastic flows of partitions
• Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve property
• The number of non-singleton blocks in Lambda-coalescents with dust

Cited by in corpus (6)

• The fixation line in the $\Lambda$-coalescent
• On the Eve property for CSBP
• From flows of Lambda Fleming-Viot processes to lookdown processes via flows of partitions
• Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve property
• The sequential loss of allelic diversity
• Kingman's coalescent with erosion