【非线性分析学术报告】

报告题目：Precise large deviations 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）

邀请人：罗海军

时间：5月4日下午15:00-16:00

地点：澳门新葡京娱乐城 425

报告摘要：Consider a sequence of independent and identically distributed random matrices $(g_n)_{n\geq 1}$ and the left random walk $G_n : = g_n \ldots g_1$ on the general linear group $GL(d, \mathbb R)$. Under suitable conditions, we establish Bahadur-Rao-Petrov type large deviation expansions for the coefficients $\langle f, G_n v \rangle$ 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 significantly the known large deviation bounds. Moreover, we prove local limit theorems with large deviations for the coefficients, and large deviation expansions under Cram\'er's  change of probability measure. For the proofs we establish the H\"older regularity of the invariant measure of the Markov chain $(\mathbb R G_n v)$ under the changed probability, which is of independent interest. Joint work with I. Grama and Q. Liu.

个人简介：中国科学院数学与系统科学研究院优秀青年副研究员。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.，Ergodic Theory Dynam. Systems，Ann. Inst. Henri Poincaré Probab. Stat.，Stochastic Process. Appl.，J. Differential Equations等。