Measure-valued and Partition-valued Processes and Random Matrices

测值过程和分值过程以及随机矩阵

• 批准号: 0071468
• 负责人: Steven Evans
• 金额: $ 17.17万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0071468&HistoricalAwards=false
• 关键词: Measure; valued; Partition; Processes; Random

0071468Evans The principal investigator studies stochastic models for evolving biological populations in which individuals interact with each other and their environment. He investigates coalescing tree processes that arise in both physical and chemical models of polymerisation, coagulation, and condensation, and in the study of stepping-stone models in population genetics. He suggests a new approach using the theory of symmetric Markov processes to the study of large random matrices that appear in particle physics and certain conjectures in number theory. He proposes a family of models originating in stochastic differential geometry for the evolution of genetic types in biological populations. The various strands of the principal investigator's work lead to a greater understanding of: the dynamics of evolving genetic profiles in large populations, general physical processes in which units clump together over time to form larger units, and a class of models in particle physics that have not only successfully explained a wide array of experimental results but also have deep connections with a number of other seemingly unrelated areas of mathematics.

0071468Evans主要研究者研究进化生物种群的随机模型，其中个体与彼此及其环境相互作用。 他研究了聚合、凝聚和冷凝的物理和化学模型中出现的聚结树过程，以及群体遗传学中的垫脚石模型研究。 他提出了一种新的方法，利用对称马尔可夫过程的理论来研究粒子物理学中出现的大型随机矩阵和数论中的某些命题。 他提出了一个家庭的模型起源于随机微分几何的进化遗传类型的生物种群。主要研究者工作的各个方面使我们更好地理解：大种群中进化遗传谱的动态，单位随时间聚集在一起形成更大单位的一般物理过程，以及粒子物理学中的一类模型，它们不仅成功地解释了大量的实验结果，而且与许多其他看似无关的领域有着深刻的联系。数学