Random Matrices and Applications

随机矩阵及其应用

• 批准号: 0457335
• 负责人: Jinho Baik
• 金额: --
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0457335&HistoricalAwards=false
• 关键词: Random; Matrices; Applications

AbstractBaikThe eigenvalues of large random matrices are known to describe thelimiting behaviors of various objects in mathematics, statisticsand physics such as random permutations, zeros of Riemann-zetafunction, sample covariance matrices, non-intersecting paths andrandom growth models. The investigator plans to study variousintrinsic properties the limiting distribution functions arisingin random matrix theory, as well as to apply the ideas and methodsof random matrix theory to probability models such as last passagepercolation, queueing models, non-intersecting paths andinteracting particle systems. Built on the investigator's andother researchers' earlier work, the long term goal is to clarifythe universality class of models which are describable in terms ofthe eigenvalues of random matrices using ideas from bothintegrable systems and probability.

大型随机矩阵的特征值描述了数学、物理和数学中各种对象的极限行为，如随机排列、Riemann-zeta函数的零点、样本协方差矩阵、不相交路径和随机增长模型等。研究者计划研究随机矩阵理论中的极限分布函数的各种内在性质，以及将随机矩阵理论的思想和方法应用于概率模型，如最后一次渗流、扩散模型、不相交路径和相互作用粒子系统。建立在调查员和其他研究人员的早期工作，长期的目标是澄清的普适性类的模型，这是描述的随机矩阵的特征值，使用的想法从bothintegrable系统和概率。