Expanding and linking random matrix theory

扩展和链接随机矩阵理论

• 批准号: DP210102887
• 负责人: Prof Peter Forrester
• 金额: $ 35.73万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2021
• 资助国家: 澳大利亚
• 起止时间: 2021-03-31 至 2024-03-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP210102887
• 关键词: Expanding; linking; random; matrix; theory

Fundamental to random matrix theory are certain universality laws, holding in scaling limits to infinite matrix size. A basic question is to quantify the rate of convergence to the universal laws. The analysis of data for the Riemann zeros from prime number theory, and of the spectral form factor probe of chaos in black hole physics, are immediate applications. An analysis involving integrable structures holding for finite matrix size and their asymptotics is proposed, allowing the rate to be quantified for a large class of model ensembles, and providing predictions in the various applied settings. The broad project is to be networked with researchers in the Asia-Oceania region, with the aim of establishing leadership status for Australia.

随机矩阵理论的基础是某些通用定律，以缩放限制到无限基质大小。 一个基本的问题是量化融合速度与普遍定律的速度。从素数理论和黑洞物理学中混乱的光谱外形探针的数据分析是直接应用。提出了涉及有限矩阵尺寸及其渐近型的可集成结构的分析，从而可以将大量模型的速率量化 合奏，并在各种应用设置中提供预测。该广泛的项目将与亚太地区的研究人员建立联系，以确立澳大利亚领导地位。