论文标题
随机基质产物的极端奇异值和GL（N，C）上的Brownian Motion
Extremal singular values of random matrix products and Brownian motion on GL(N,C)
论文作者
论文摘要
我们建立了具有正确单位不变分布的随机矩阵产物的最大奇异值，在一个制度下，矩阵因子的数量和矩阵的大小往往同时无限。最大的对数奇异值的行为与Dyson Brownian运动的n个极限相吻合，其特征漂移矢量由相同间隔的坐标组成，该坐标均与GL（N，C）上Brownian Motion的最大对数奇异值的大n极限相匹配。我们的方法利用多元贝塞尔生成函数（也称为球形变换）的形式主义获得和分析组合表达式以观察到这些过程。
We establish universality for the largest singular values of products of random matrices with right unitarily invariant distributions, in a regime where the number of matrix factors and size of the matrices tend to infinity simultaneously. The behavior of the largest log singular values coincides with the large N limit of Dyson Brownian motion with a characteristic drift vector consisting of equally spaced coordinates, which matches the large N limit of the largest log singular values of Brownian motion on GL(N, C). Our method utilizes the formalism of multivariate Bessel generating functions, also known as spherical transforms, to obtain and analyze combinatorial expressions for observables of these processes.
