AF: Small: Random Processes, Statistical Physics and Computation

AF：小：随机过程、统计物理和计算

• 批准号: 1420934
• 负责人: Alistair Sinclair
• 金额: $ 44.97万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-07-01 至 2018-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1420934&HistoricalAwards=false
• 关键词: AF; Small; Random; Processes; Statistical

The project is concerned with the quantitative analysis of random and physical processes, viewed both as application areas where techniques from theoretical computer science can be useful, and as an impetus that suggests novel directions for CS theory.  In addition to core research topics in theoretical computer science (algorithms and computational complexity), the project makes connections with the fields of probability and statistical physics by examining them through the "computational lens."Specifically, the project will address the following two broad themes:1. Random processes with an algorithmic flavor: the rigorous study of iterative algorithms for matrix pre-conditioning that are widely used in numerical linear algebra but poorly understood theoretically; the analysis of certain fundamental Markov chains that are beyond the range of current techniques; and the understanding, from a computational viewpoint, of non-linear stochastic processes known as "quadratic dynamical systems," which generalize the classical Boltzmann equation in physics and models for recombination in population genetics.2. Computational aspects of statistical physics: the development of more sophisticated techniques for studying the key property of spatial mixing in spin systems and its algorithmic implications; the investigation of stability properties of naturally occurring combinatorial polynomials (partition functions) in statistical physics, and their applications to algorithms and computational complexity; and the potential application of models from statistical physics to the study of phenomena such as viral marketing in social networks.Broader impacts of the project include graduate student training in the interdisciplinary field of theoretical computer science, statistical physics and applied probability.

该项目涉及对随机和物理过程进行的定量分析，重新计算机可能是有用的CAL计算机科学（算法和计算复杂性），它们通过“具体来说，该项目将解决以下两个广泛的主题：1。与随机过程有关HMIC风味：对基质预处理的严格研究LS中的经典Boltzmann方程在人群遗传学中​​。 ，以及从统计物理学到该项目的现象的模型的算法和计算竞争；