Expanding and linking random matrix theory

随机矩阵理论的基础是某些普适性定律，在无限矩阵大小的尺度限制中保持不变。 一个基本的问题是量化的速度收敛到普遍的法律。从素数理论的黎曼零点的数据分析，和黑洞物理学中的混沌的频谱形状因子探针，是直接的应用。提出了一种包含有限矩阵大小的可积结构及其渐近性的分析方法，使得对大类模型的速率可以量化 合奏，并在各种应用设置提供预测。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。

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.