Probability

可能性

• 批准号: 1000230566-2014
• 负责人: Perkins, Edwin
• 金额: $ 14.57万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=694487
• 关键词: Probability

The Central Limit Theory states that a large sum of small contributions will beclose to the normal distribution irrespective of the nature of the individual contributions. I study an analogue of this universality for random spatial systems. The large scale space-time behaviour of random systems exhibiting critical growth often approximates a stochastic process called Super-Brownian motion. The approximating systems include epidemic models, competing species models in mathematical ecology, percolation in statistical physics, or allele frequencies in population genetics. My research focuses on using this universality to study many of these interacting spatial systems and on extending this universal correspondence.

中心极限理论指出，无论个体贡献的性质如何，大量的小贡献都将接近正态分布。我研究了随机空间系统的这种普遍性的模拟。随机系统的大尺度时空行为表现出临界增长，通常近似于一个称为超布朗运动的随机过程。近似系统包括流行病模型，数学生态学中的竞争物种模型，统计物理学中的渗流，或群体遗传学中的等位基因频率。我的研究重点是利用这种普遍性来研究许多这些相互作用的空间系统，并扩展这种普遍的对应关系。