Measure-Valued Processes: Coagulation and Coalescence

9703845考虑了两类具有凝聚性的测值随机过程。第一类过程的成员描述了随着时间流逝，通过二元碰撞的随机序列对质量集合的聚集。已知的构造结果被推广到新的碰撞机制和更一般的初始质量构型。研究了在不同的极限状态下的渐近行为。第二类过程的成员是各种空间过程(如踏脚石模型和长程投票者模型)的时空重标度极限，并被定义为对由聚合马尔可夫过程系统诱导的标号划分过程的对偶。研究了这类模型样本路径性质的几个问题。首席调查员将研究两个涉及粒子聚合的数学模型。第一类模型已应用于聚合等化学现象和凝聚和凝聚的物理现象，如引力作用下星系团的演化。此外，还与数据库建设中考虑的问题有关。拟议的研究特别涉及理解当一个人考虑具有极大量合并对象的系统时会发生什么，这在应用程序中通常是这样的。第二类模型起源于生态学和种群遗传学，当人们想要描述具有大量流动个体的地理结构的种群的进化时。

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.