报告题目：Large deviation expansions for the coefficients of random walks on the general linear group

报 告 人：肖惠副研究员（中国科学院数学与系统科学研究院）

报告时间：2023年3月29日  10:45

报告地点：数学研究中心528

报告摘要：

Consider $(g. n)_ ,(n\geq 1}$ a sequence of independent and identically distr ibuted random matrices and the left random walk $G_n:=g_ n\ldotsg_ .1$ on the general linear group $GL(d, \mathbb R)$. Under suitable conditions, we establish Bahadur -Rao-Petrov type large deviation expansions for the coefficients $\langle f, G. _nv \rangle$ of the product $G_ n$, where $v \in \mathbb R' °d$ and $f \in (\mathbb R^d) ^*$. In particular, we obtain an explicit rate function in the large deviation principle, thus improving significant ly the known lar ge deviation bounds. Moreover, we prove local limit theorems with large deviations for the coefficients, and large deviation expansions under Cram\'er's change of probility measure. For the proofs we establish the H\"older regularity of the invar iant measure of the Markov chain $(\mathbb RG_ n v)$ under the changed probability, which is of independent interest. Joint work with 1. Grama and Q. Liu.

报告人简介：

肖惠，中国科学院数学与系统科学研究院优秀青年副研究员。2013年本科毕业于湖南师范大学数学与应用数学专业。2020年博士毕业于法国南部列塔尼大学，2020年到2023年在德国希尔德斯海姆大学做博士后。主要研究方向为随机矩阵乘积、（分枝）随机游动。相关论文发表（含接受发表）在J. Eur. Math. Soc., Ann. Probab., Ann. Inst. Henri Poincare Probab. Stat., Stochastic Process. Appl., Ergodic Theory Dynam. Systens, J. Differential Equations等。