Speaker: Su Zhonggen, Professor, School of Mathematical Sciences, Zhejiang University

Date: Mar 2, 2022

Time: 19:00

Location: Zoom ID: 742 475 3864

Sponsor: Research Center for Mathematics and Interdisciplinary Sciences, Shandong University

Research Center for Nonlinear Expectation

Abstract:

It has been a most fundamental issue to describe concentration phenomenon of a probability measure or a random variable in the theory of probability. The first remarkable result, often attributed to Bienaym´e (1853) and Chebyschev (1867), characterizes the dispersion of a random variable away from its mean by putting an upper bound on the probability. The inequality is unfortunately so weak as to be virtually useless to anyone looking for a precise statement on the probability of a large deviation. A sustained huge effort have indeed been made to develop a tighter, and even optimal upper bound for a specific probability measure (random variable) in the past century. In this talk, I will first give a brief review of common concentration inequalities in probability theory, in particular, the classic Chernoffff argument for optimal upper bounds of exponential form. And then I turn to a (relatively) recent distinguished result due to Talagrand in the product space in 1990s, and illustrate its utility by looking at the longest increasing subsequences.

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https://www.view.sdu.edu.cn/info/1020/162509.htm