几何分析讨论班—Critical radius and supremum of random spherical harmonics
主 题: 几何分析讨论班—Critical radius and supremum of random spherical harmonics
报告人: 冯仁杰 (北京国际数学研究中心)
时 间: 2017-03-15 14:00-16:00
地 点: 理科1号楼1114
Abstract: We first consider deterministic immersions of the d-dimensional sphere into high dimensional Euclidean spaces, where the immersion is via spherical harmonics of level n. The main result of the article is the, a priori unexpected, fact that there is a uniform lower bound to the critical radius of the immersions as n→∞. This fact has immediate implications for random spherical harmonics with fixed L2-norm. In particular, it leads to an exact and explicit formulae for the tail probability of their suprema by Weyl's tube formula, and also relates this to the expected Euler characteristic of their upper level sets. We will mainly concentrate on the geometry aspect of the program, such as Weyl's tube formula in the integral geometry. The talk is very elementary and accessible to all students. This is the joint work with R. Adler.