LARGE DEVIATIONS FOR PRODUCTS OF RANDOM MATRICES
报告题目(Title)：LARGE DEVIATIONS FOR PRODUCTS OF RANDOM MATRICES
报告人(Speaker)：Quansheng LIU (Universite de Bretagne -Sud)
地点(Place)：后主楼1124
时间(Time)：2019年12月13日 14：30-15：30
邀请人(Inviter)：高志强
报告摘要
Let (g_n)n\geq1 be a sequence of independent identically distributed d×d real random matrices with Lyapunov exponent. We are interested in asymptotic properties of the random walk {Gnx}n\geq0 governed by the products G_n := g_n...g_1 of random matrices, starting with G_0x := x on the unit sphere in R^d. The position G_nx of the walk at time n is characterized by the norm |G_nx| and the direction X^x_n = G_nx=|G_nx|. We establish precise asymptotics for the large deviation probability P(log |G_nx| \geq n(q +l)), where q > \gamma is fixed and l = l(n) \to 0 as n \to1, for both invertible matrices and positive matrices; we also prove analogous results for the couple (X^x_n; log |G_nx|) with target functions \phi on X^x_n and on log |Gnx|. As applications we improve previous results on the large deviation principle for the matrix norm \|Gn\|, and obtain a precise local limit theorem with large deviations. (Based on a joint work with Ion Grama and Hui Xiao.)
主讲人简介
Liu Quansheng(刘全升)教授，法国南布列塔尼大学一级教授，大西洋布列塔尼数学实验室主任。主要研究方向为概率论及概率方法在图像处理方面的应用。在分枝过程等问题和图像处理方面取得了许多重要成果。已发表SCI文章八十多篇，被引用六百多次。刊载文章的期刊包括了Stochastic Process. Appl., J. Math. Anal. Appl., Ann. Inst. H. Poincaré Probab. Statist., Bernoulli, Ann. Appl. Probab., Probability Theory and Related Fields等概率方向重要期刊以及J. Sci. Comput. IEEE Trans. Image Process.等信息科学方向重要期刊。
