一、题目

Some Recent Advances on Tracy-Widom Laws and Airy Processes

二、主讲人

苏中根

三、摘要

The 2020 Steele Prize for Seminal Contribution to Research in Analysis/Probability Theory was awarded to C.Tracy and H. Widom for the paperLevel-spacing distributions and the Airy kernel. Comm. Math. Phys. (1994). In this introductory talk I shall fifirst describe the origins of Tracy-Widom distributions, their important features, recent advances and some open problems. The Airy processes are a collection of stochastic processes which are usually defifined through fifinite dimensional distributions, and whose one-dimensional marginal is Tracy-Widom distribution or the like. Compared to well-studied Gaussian processes, these are newly-born challenging processes. However, there have been some remarkable results around their long and short-range correlation, local Brownian properties, continuity modulus of sample paths in the past years. In the second part of this talk we shall describe some typical models in which Airy processes naturally arise, and review a few representative approaches in the study of Airy processes. The research fifield aroused by Tracy-Widom’s seminal paper is rapidly growing at an exponential rate and the literature is huge, so this talk will focus on the topics from my personal research taste.

四、主讲人简介

苏中根，浙江大学教授，博士生导师。 1995年获复旦大学理学博士学位， 主要从事概率极限理论及其应用研究，最近研究兴趣包括高维随机矩 阵的渐近谱理论，随机增长过程极限性质。《概率极限理论基础》（林正炎、陆传荣、苏中根）作为研究生教材，2002年获教育部普通高校优秀教材一等奖，2021年（第二版）获首届全国优秀教材（高等院校）二等奖。

五、时间

9月15日（周三） 9:00-11:00

六、地点

腾讯会议 ，会议ID : 409 645 735

七、主办方

非线性期望前沿科学中心

数学与交叉科学研究中心