Lambda-coalescent processes and genealogies

The talk concerns several aspects of a class of stochastic coalescent processes. These coalescents arise as scaling limits in mathematical population genetics models. They are ``duals" to measure-valued processes known as (generalized) Fleming-Viot processes. In special cases the correspondence between the genealogical process of a (super) diffusion and a coalescent process is well known. The spatial (or structured) coalescents are particularly important in the study of asymptotic behavior of a class of interacting particle systems and the corresponding scaling limits.

I will attempt to describe most of the above relations in the intuitive ``particle representation" setting. Some interesting properties of (spatial) Lambda-coalescents will be discussed, as well as very interesting consequences for the asymptotics of the related interacting particle systems and their scaling limits.

Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).