Brownian Motion and Combinatorial Stochastic Processes

该项目将继续对大型有限集合上的组合结构理论(如树、森林、映射和划分)和布朗运动理论以及相关过程(如布朗游程、布朗桥和具有独立增量的过程)之间的深层联系进行持续的研究。具体的研究课题包括再生合成结构，碎裂和凝聚过程，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的分布。该项目的成果预计将包括随机分割和分割值过程的新模型，特别是碎裂和凝聚过程，这可能在许多以前应用过此类过程的领域中具有价值，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.