Emma Horton: A binary branching model with Moran-type interactions

Abstract

Branching processes naturally arise as pertinent models in a variety of applications such as population size dynamics, neutron transport and cell proliferation kinetics. A key result for understanding the behaviour of such systems is the Perron Frobenius decomposition, which allows one to characterise the large time average behaviour of the branching process via its leading eigenvalue and corresponding left and right eigenfunctions. However, obtaining estimates of these quantities can be challenging, for example when the branching process is spatially dependent with inhomogeneous rates. In this talk, I will introduce a new interacting particle model that combines the natural branching behaviour of the underlying process with a selection and resampling mechanism, which allows one to maintain some control over the system and more efficiently estimate the eigenelements. I will then present the main result, which provides an explicit relation between the particle system and the branching process via a many-to-one formula and also quantifies the L^2 distance between the occupation measures of the two systems. Finally, I will discuss some examples in order to illustrate the scope and possible extensions of the model, and to provide some comparisons with the Fleming Viot interacting particle system. 

This is based on ongoing work with Alex Cox (University of Bath) and Denis Villemonais (Université de Lorraine).