Mathematical Sciences: Research in Random Matrices and Spectral Asymptotics

数学科学：随机矩阵和谱渐近学研究

• 批准号: 9424292
• 负责人: Harold Widom
• 金额: $ 10.5万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9424292&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Random; Matrices

Widom DMS-9424292 Widom has shown that there are differential equations associated with important random matrix models, and has used this fact to obtain explicit expressions for various quantities arising in the theory. He will continue this investigation to determine the extent to which the results apply to classes of models satisfying some common conditions. One class of deterministic problems deals with the asymptotics of the eigenvalues of finite Toeplitz matrices and their analogues. Each of these has an associated "symbol," and one expects to relate the distribution of eigenvalues to the values of the symbol. This proposal concerns the applications of operator theory to random matrix models. In random matrix theory fundamental quantities that arise naturally are often related to determinants of certain operators. The asymptotic behavior of these determinants is of independent interest in operator theory.

Widom DMS-9424292 Widom 表明存在与重要随机矩阵模型相关的微分方程，并利用这一事实获得了理论中出现的各种量的显式表达式。 他将继续这项调查，以确定结果在多大程度上适用于满足某些常见条件的模型类别。 一类确定性问题涉及有限托普利茨矩阵及其类似物的特征值的渐近性。 其中每一个都有一个相关的“符号”，人们期望将特征值的分布与符号的值联系起来。 该提案涉及算子理论在随机矩阵模型中的应用。 在随机矩阵理论中，自然出现的基本量通常与某些算子的行列式有关。 这些行列式的渐近行为在算子理论中具有独立的意义。