论文标题
随机矩阵动态的通用性
Universality of random matrix dynamics
论文作者
论文摘要
我们讨论了宽度与间距比的概念，该概念在描述了随机矩阵的乘法和加性随机过程中进化运算符的局部光谱统计中起着核心作用。我们表明，局部光谱特性是高度通用的，并且取决于单个参数是宽度与间距比。我们讨论了dysonian布朗运动的内核与lyapunov矩阵的内核之间的二元性，用于Ginibre矩阵的产物。
We discuss the concept of width-to-spacing ratio which plays the central role in the description of local spectral statistics of evolution operators in multiplicative and additive stochastic processes for random matrices. We show that the local spectral properties are highly universal and depend on a single parameter being the width-to-spacing ratio. We discuss duality between the kernel for Dysonian Brownian motion and the kernel for the Lyapunov matrix for the product of Ginibre matrices.
