图 书 馆
随机球面特征函数几何的一些最新进展Some Recent Developments on the Geometry of Random Spherical Eigenfunctions |
|
| 课程网址: | http://videolectures.net/8ecm2021_marinucci_some_recent/ |
| 主讲教师: | Domenico Marinucci |
| 开课单位: | 罗马大学 |
| 开课时间: | 2021-07-06 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | A lot of efforts have been devoted in the last decade to the investigation of the high-frequency behaviour of geometric functionals for the excursion sets of random spherical harmonics, i.e., Gaussian eigenfunctions for the spherical Laplacian ∆S2 . In this talk we shall review some of these results, with particular reference to the asymptotic behaviour of variances, phase transitions in the nodal case (the Berry’s Cancellation Phenomenon), the distribution of the fluctuations around the expected values, and the asymptotic correlation among different functionals. We shall also discuss some connections with the Gaussian Kinematic Formula, with Wiener-Chaos expansions and with recent developments in the derivation of Quantitative Central Limit Theorems (the so-called Stein-Malliavin approach). |
| 关 键 词: | 高斯特征函数; 贝里抵消现象; 维纳-混沌展开式 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2022-03-27：hqh |
| 最后编审: | 2022-03-27：hqh |
| 阅读次数: | 26 |