Measure-Valued Processes: Coagulation and Coalescence

小行星9703845 本文考虑了两类测度值随机过程，这两类测度值随机过程具有共同的聚并特征。 第一类过程的成员描述了集群作为一个集合的质量通过一个随机序列的二进制碰撞的时间推移。 已知的建设结果扩展到新的碰撞机制和更一般的初始质量配置。 渐近行为研究在各种限制制度。 第二类过程的成员是各种空间过程（如垫脚石模型和长程投票模型）的时空尺度限制，并且被定义为与由合并马尔可夫过程系统引起的标记划分过程“对偶”。 研究了这类模型的样本路径性质。 主要研究者将研究两个涉及颗粒聚结的数学模型。 第一类模型已被应用于化学现象，如聚合和物理现象的凝聚和冷凝，如星系团的引力演化。 也有与数据库建设中考虑的问题的连接。 拟议的研究特别涉及理解当人们考虑具有极大量合并对象的系统时会发生什么，这在应用中通常是这样。 当人们希望描述具有大量移动的个体的地理结构种群的进化时，第二类模型起源于生态学和种群遗传学。

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.