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Generalized 4 moment Theorem with Application to Random Matrix Theory
澳门新葡8455最新网站:2019年11月15日 17:16 点击数:

报告人:白志东

报告地点:澳门新葡8455最新网站6楼大应用数学实验室

报告澳门新葡8455最新网站:2019年11月20日星期三13:30-14:30

邀请人:张凯军

报告摘要:

Many results in random matrix theory show universality, that is, the result is true for all distributions provided that their first 4 moments are matching with normal distribution. On the other hand, the universality provides an approach to investigate properties of RMT, that is, show universality first, then investigate the property under normality assumption. Recently, Tao and Vu proved a FMT for Wigner matrix. But they assumed much heavy assumptions, say the condition C0. Now, we consider the CLT for normalized spiked eigenvalues, we shall show FMT fifirst and then investigate the CLT of spiked eigenvalues. Because we only assume the match of first two moments and a proper of tail probability, x4P(|Xij | > x) → 0, which implies all moments less than 4 exist but the 4th moment may not exist. So, we call it G

主讲人概况:

白志东,第三世界科新葡京最新官网院士,教育部自然科学一等奖和国家自然科学二等奖获得者。澳门新葡8455最新网站特聘教授。现在担任《Random Matrix: Theory and Applications》创刊主编,《Journal of statistical planning and inference》,《Statistical Papers》,《Journal of Probability and Statistics》,《Sankya》等杂志副主编;曾担任《Journal of Multivariate Analysis》主编, 《StatisticaSinica》副主编,中国概率统计学会常务理事。至今已发表学术论文220余篇,其中160多篇为SCI检索论文,另有10多篇乃应邀为各学术专著所写的章节。论文已被SCI引用近2200余次。白志东建立的“白志东不等式”和“经验谱分布收敛速度的估计”,给经验谱分布收敛速度的估计开创了一种方法,并且对Wigner矩阵和大维样本协方差矩阵之经验谱分布给出了初步的收敛速度之估计。首次提出 “Partial Cramer条件”的概念,填补了没有Cramer条件不能渐近展开的空白。

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