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【ag平台网址学术报告】几何测度论与相关领域讨论班
ag平台网址:2019-12-11  浏览量:

LARGE DEVIATIONS FOR PRODUCTS OF RANDOM MATRICES

刘全升 教授

(法国南布列塔尼大学

报告时间:201912月12日 (星期四) 下午14:00-15:00

报告地点:新主楼F222

报告摘要:Let (gn)n≥1 be a sequence of independent identically distributed d × d real random matrices with Lyapunov

exponent γ. We are interested in asymptotic properties of the random walk {Gnx}n≥0 governed by the products Gn = gn ...g1 of random matrices, starting with G0x = x on the unit sphere in Rd. The position Gnx of the walk at time n is characterized by the norm |Gnx| and the direction Xnx = Gnx/|Gnx|. We establish precise asymptotics for the large deviation probability P(log |Gnx| ≥ n(q + l)), where q > γ is fixed and l = l(n) → 0 as n → ∞, for both invertible matrices and positive matrices; we also prove analogous results for the couple (Xnx,log|Gnx|) with target functions φ on Xnx and ψ 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.)

报告人概况:刘全升,巴黎第六大学概率论专业博士,现为南布列塔尼大学数学系主任,法国国家一级终身教授,享受法国国家优秀科研奖金,多次任中国教育部“长江学者”通讯评审专家, 和新世纪数学奖通讯评审专家。刘全升教授主要从事概率统计理论、分形几何及数字图像处理等领域的研究, 在国内外高水平期刊发表论文近90余篇,其研究成果受到业界的广泛认可。

邀请人: 梁湘玉

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