一、报告题目

Concentration Inequalites of Measures: From Chernoffff to Talagrand

二、主讲人

苏中根

三、报告时间

2022年3月2日 19:00

四、报告地点

zoom: 742 475 3864

五、摘要

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 fifirst 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 efffforts have indeed been made to develop a tighter, and even optimal upper bound for a specifific probability measure (random variable) in the past century. In this talk, I will fifirst 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.

六、主讲人简介

苏中根，浙江大学教授，博士生导师。1995年获复旦大学博士学位，主要从事概率极限理论及其应用研究，发表学术论文50余篇，出版教材和专著4本。曾主持国家自然科学基金面上项目5项、教育部博士点专项基金 (导师类) 项目1项，浙江省自然科学基金杰出青年团队项目1项等。科研成果“概率极限理论及其在Gauss过程轨道性质方面的应用 (与林正炎、张立新合作)”2003年获教育部科技进步二等奖；《概率极限理论基础》(与林正炎、陆传荣合著) 2021年获首届国家优秀教材二等奖，2002年荣获全国普通高校优秀教材一等奖；《概率论》(与林正炎、张立新合著) 被列为“十一五”、“十二五”国家级规划教材，2013年获浙江大学首届十大教材，2017年获浙江省“十二五”高等学校优秀教材奖。

七、主办单位

非线性期望前沿科学中心

数学与交叉科学研究中心