Measure-Valued Processes: Coagulation and Coalescence

考虑了两类具有聚并的共同特征的测度值随机过程。第一类过程的成员描述了随着时间的推移，由随机的二元碰撞序列形成的质量集合的聚集。已知的构造结果扩展到新的碰撞机制和更一般的初始质量构型。研究了各种极限域下的渐近行为。第二类过程的成员是各种空间过程（如踏脚石模型和远程选民模型）的时空重标极限，并被定义为对由聚并马尔可夫过程系统诱导的标记划分过程的“对偶”。研究了这类模型样本路径性质的几个问题。首席研究员将研究两个涉及粒子聚并的数学模型。第一类的模型已经应用于化学现象，如聚合和物理现象，如星系团在引力作用下的演化。这也与数据库建设中所考虑的问题有关。拟议的研究特别涉及理解当一个人考虑具有大量合并对象的系统时会发生什么，这通常是应用程序中的情况。第二类模型起源于生态学和种群遗传学，当人们希望描述具有大量流动个体的地理结构种群的进化时。

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.