一、报告题目

Complexity of Gaussian random fields with isotropic increments

二、主讲人

曾强

三、报告时间

2022年8月16日10:00-12:00

四、报告地点

腾讯会议ID：752 465 434

五、摘要

Random fields with isotropic increments were introduced by Kolmogorov in the 1940s. Gaussian random fields on N-dimensional Euclidean spaces with isotropic increments were classified as isotropic case and non-isotropic case by Yaglom in the 1950s. Such models were used widely in statistical physics. In particular, they were introduced to model a single particle in a random potential by Engel, Mezard and Parisi in 1990s. A basic question is to count the number of critical points (or local minima, saddles) of the fields, which is commonly known as complexity. In 2004, Fyodorov computed the large N limit of expected number of critical points for isotropic Gaussian random fields. In this talk, I will present some results on the large N behavior of complexity of non-isotropic Gaussian random fields with isotropic increments. Connection to random matrices and large deviations will be explained. This talk is based on joint works with Antonio Auffinger (Northwestern University) and Hao Xu (University of Macau).

六、主讲人简介

曾强，现任澳门大学数学系助理教授；本科毕业于北京师范大学，博士毕业于伊利诺伊大学香槟分校，其后在哈佛大学、伯克利国家数学科学研究所以及美国西北大学做博士后，然后在纽约城市大学皇后学院任tenure-track助理教授。研究方向是非交换概率、自旋玻璃和随机矩阵等；研究论文发表于CPAM，CMP，AOP，PTRF，JFA，IMRN，JLMS等期刊。

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