受学校国际合作处资助，法国南布列塔尼大学刘全升教授在公司作线上专题报告，欢迎感兴趣的师生参加。

时间：7月9日，下午16:55-17:40

腾讯会议号：981 957 685

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题目：Convergence rate in the central limit theorem and precise moderate deviations for products of random matrices

摘要：Let gn be independent and identically distributed d×d real random matrices. Let Gn = gn…g1 be the product matrix. Consider the random walk Gnx and its direction Xnx = Gnx/|Gnx|, n ≥ 1, where |.| is an arbitrary norm in Rd and x is a starting point in Rd with |x| = 1. For both invertible matrices and positive matrices, under suitable conditions we prove a Berry-Esseen type bound and an Edgeworth expansion for the couple (Xnx, log |Gnx|), about the rate of convergence in the central limit theorem. These results are established using a new smoothing inequality on the complex plane, the saddle point method and spectral gap properties of the transfer operator related to the Markov chain Xnx. Cramér type moderate deviation expansions as well as a local limit theorem with moderate deviations are also proved for the couple (Xnx, log |Gnx|) with a target function φ on the Markov chain Xnx. As an example of applications, we establish the Berry-Esseen type bound and the Cramér type moderate deviation expansion for a multi-type branching process in a random environment (MBPRE), using the Kesten-Stigum type theorem that we found recently, which enables us to compare precisely a MBPRE with the products of the conditional mean matrices.

报告人简介：

刘全升，法国国家一级终身教授，现任南布列塔尼大学数学系主任。1980年进入武汉大学数学系学习，先后连续经历本科、硕士和博士研究生阶段。1989年11月进入巴黎第六大学深造；1991-1992学年任巴黎第九大学助教；1992-1993学年任法国雷恩应用科学所助教。1993年2月获得巴黎第六大学概率论专业博士文凭。1993至2000年任法国雷恩大学讲师、副教授。2000年1月获得指导博士研究资格，同年9月起任法国南布列塔尼大学教授。曾任南布列塔尼大学行政议会成员，科技议会成员和专家评委，数学系计算机与统计学院副经理，数学与应用数学专业研究生工作负责人。2007年起任南布列塔尼大学数学系主任。主要研究方向为：概率论；分形几何；数字图像处理。