Measure-Valued Processes: Coagulation and Coalescence

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9703845 Evans Two classes of measure-valued stochastic processes are considered that possess the common feature of coalescence. Members of the first class of processes describe the clustering as time passes of a collection of masses by a random sequence of binary collisions. Known construction results are extended to new collision mechanisms and more general initial mass configurations. Asymptotic behavior is studied in various limiting regimes. Members of the second class of processes are space-time rescaling limits of a variety of spatial processes such as stepping-stone models and long range voter models, and are defined to be "dual" to the labeled partition process induced by a system of coalescing Markov processes. Several questions concerning the sample path properties of such models are investigated. The Principal Investigator will study two mathematical models involving coalescence of particles. Models in the first class have been applied to chemical phenomena such as polymerisation and physical phenomena of coagulation and condensation such as the evolution of galactic clusters by gravitational attraction. There are also connections with questions considered in the construction of data bases. The proposed research deals particularly with understanding what happens when one considers systems with extremely large numbers of coalescing objects, as is usually the case in applications. Models in the second class have their origins in ecology and population genetics when one wishes to describe the evolution of geographically structured populations with large numbers of mobile individuals.