Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	刘全升教授, 法国Université Bretagne-Sud
Inviter:
Title:	Products of random matrices
Language:	Chinese
Time & Venue:	2023.03.01 14:00-15:00 南楼N202
Abstract:	Let $(g_n)_{n\geq 1}$ be a sequence of independent and identically distributed random matrices of type $d \times d $ with real coefficients. Consider the products $G_n : = g_n \ldots g_1$ and the random walk $(G_n x)_{n\geq 1}$ in $\mathbb R^d$, where $x\in {\mathbb R}^d$ is the starting point. We are interested in asymptotic properties of the operator norm $\\| G_n\\|$, the vector norm $\|G_n x\|$, the coefficients $G_n^{i,j}$ (the $(i,j)$-th entry of $G_n$), and the spectral radius $\rho(G_n)$ of $G_n $, as $n \rightarrow \infty$. Precise large and moderate deviation results of type Baradur-Rao and Cramér will be presented. Berry-Esseen bound and Edgeworth expansion about the rate of convergence in the central limit theorem will also be considered. (Mainly based on joint works with Ion Grama and Hui Xiao: J. Eur. Math. Soc. 2022, Ann. Prob. 2023, Stochastic Proc. Appl. 2023.)