Brownian Motion and Combinatorial Stochastic Processes

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

0405779 Pitman The project will continue an ongoing study of deep connections between the theory of combinatorial structures on a large finite set, such as trees, forests, mappings, and partitions, and the theory of Brownian motion and related processes such as Brownian excursion, Brownian bridge, and processes with independent increments. Specific topics to be studied include regenerative composition structures, processes of fragmentation and coagulation, tree-valued stochastic processes, asymptotics of uniform random spanning trees, and the distribution of homogeneous functionals of Brownian motion. Results of the project are expected to include new models for random partitions and partition-valued processes, particularly processes of fragmentation and coagulation, which may be of value in the numerous fields where such processes have been applied before, including physics, astronomy, genetics, and ecology.