Recent progress in coalescent theory

Abstract

Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications to theoretical population genetics and other fields such as spin glass models. The emphasis is on recent work concerning in particular the connection of these processes to continuum random trees and spatial models such as coalescing random walks.

Lecture notes, to appaear in the collection "Ensaios Matematicos". 17 figures

References in corpus (6)

• Differential equation approximations for Markov chains
• A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks
• Kingman's coalescent and Brownian motion
• An example of Brunet-Derrida behavior for a branching-selection particle system on $\mathbb{Z}$
• Effect of Noise on Front Propagation in Reaction-Diffusion equations of KPP type
• Coagulation, diffusion and the continuous Smoluchowski equation