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.

随机矩阵理论的基本原理是一定的普适性定律，在无限大的矩阵大小上有定标限制。一个基本的问题是量化趋同于普遍规律的速度。对素数理论中黎曼零点的数据分析，以及对黑洞物理中混沌的光谱形状因子探测的数据分析，都是直接的应用。提出了一种关于有限矩阵大小的可积结构及其渐近性的分析，允许对一大类模型的速度进行量化。 合奏，并在各种应用环境中提供预测。这个广泛的项目将与亚洲-大洋洲地区的研究人员联网，目的是确立澳大利亚的领导地位。