Measure-valued and Partition-valued Processes and Random Matrices

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

0071468 Evans The principal investigator studies stochastic models for evolving biological populations in which individuals interact with each other and their environment. He investigates coalescing tree processes that arise in both physical and chemical models of polymerisation, coagulation, and condensation, and in the study of stepping-stone models in population genetics. He suggests a new approach using the theory of symmetric Markov processes to the study of large random matrices that appear in particle physics and certain conjectures in number theory. He proposes a family of models originating in stochastic differential geometry for the evolution of genetic types in biological populations. The various strands of the principal investigator's work lead to a greater understanding of: the dynamics of evolving genetic profiles in large populations, general physical processes in which units clump together over time to form larger units, and a class of models in particle physics that have not only successfully explained a wide array of experimental results but also have deep connections with a number of other seemingly unrelated areas of mathematics.