Brownian Motion and Combinatorial Stochastic Processes

[405776 .皮特曼]该项目将继续研究大有限集上的组合结构理论（如树、森林、映射和分区）与布朗运动理论和相关过程（如布朗偏移、布朗桥和具有独立增量的过程）之间的深层联系。具体的研究课题包括再生组合结构，破碎和凝聚过程，树值随机过程，均匀随机生成树的渐近性，以及布朗运动的齐次泛函分布。该项目的结果预计将包括随机分区和分区值过程的新模型，特别是破碎和凝固过程，这可能在许多领域有价值，这些领域之前已经应用了这些过程，包括物理学、天文学、遗传学和生态学。

0405779Pitman 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.