报告题目：The Riemann Hypothesis and Stein's Method
 
报 告 人：Prof. Qi-Man SHAO (The Chinese University of Hong Kong)
 
报告时间：5月20日下午15：00（周五）
 
报告地点：知新楼B-1238
 
 
 
Abstract: The Rieman hypothesis is a well-known open question and there are many equivalent statements. One equivalent conjecture is that the moment generating function of a special probability density function, say , haspure imaginary zeros. So the conjecture is reduced to nd a sequence of random variables whose moment generating functions have pure imaginary zeros and their limiting probability density function is   . It was proved by Lee-Yang (1952) that the moment generating function of Ising models has pure imaginary zeros. Therefore, if one cannd a sequence of Ising models so that the limiting probability density function is , then the Riemann Hypothesis holds. In this talk we shall use Stein's method to give a concrete approach to identify the limiting distribution for any given sequence of Ising models. The problem can be reduced to calculate conditional expectations and conditional variances.

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