Iterated Function Systems, Random Analytic Functions and Random Matrices (C06)

在这个项目中，我们研究了随机函数的各个方面，重点是随机动力系统，随机解析函数和随机依赖项的随机矩阵的谱性质。对于随机解析函数，我们感兴趣的是其零点的全局和局部行为，而在随机矩阵理论中，我们将集中于全局和局部特征值统计量。对于迭代随机函数，系统地研究这种在状态空间端点渐近线性的随机动力系统将成为一个新的重点。

In this project, we study aspects of random functions with a focus on random dynamical systems, random analytic functions and spectral properties of random matrices with stochastically dependent entries. Regarding random analytic func- tions, we are interested in the global and local behavior of their zeros, while in random matrix theory, we will concentrate on global and local eigenvalue statis- tics. As for iterated random functions, a new focus will be the systematic study of such random dynamical systems that are asymptotically linear at the endpoints of their state space.