Topics in random matrix theory and spectral theory of operators on Riemannian manifolds.

随机矩阵理论和黎曼流形算子谱理论的主题。

• 批准号: EP/H023127/1
• 负责人: Yang Chen
• 金额: $ 2万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2009
• 资助国家: 英国
• 起止时间: 2009 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FH023127%2F1
• 关键词: Topics; random; matrix; theory; spectral

Large systems consisting of many elementary components obeying simple binary interaction rule are very effectiverepresentatives of complex systems. As the number of constituents increases collective behaviour involving largenumber of the elementaries emerges. It turns out that eigenvalues of large random matrices --- square array of numbers drawn with theaid of the throw of a die (which accounts for the randomness) and itscontinuous generalization involving differentiation---also behave in a similar manner. In these projects the behaviour of thethe eigenvalues in both instances will give value insights into the model complex systems.

由许多符合简单二元相互作用规则的基本组件组成的大型系统对复杂系统非常有效。随着成分的数量增加了涉及小学的劳力器的集体行为。事实证明，大型随机矩阵的特征值 - - 绘制的数字平方阵列，以抛出模具的投掷（这是随机性）及其连续的概括涉及分化的 - 也以类似的方式行事。在这些项目中，在这两种情况下，特征值的行为都将为模型复杂系统提供价值见解。

项目成果

PDEs satisfied by extreme eigenvalues distributions of GUE and LUE

• DOI: 10.1142/s2010326311500031
• 发表时间: 2011-02
• 期刊: arXiv: Mathematical Physics
• 作者: E. Basor;Yang Chen;Lun Zhang