On the Correlation of Critical Points and Angular Trispectrum for Random Spherical Harmonics

被引：2
作者：
Cammarota, Valentina [1 ]
Marinucci, Domenico [2 ]
机构：
[1] Sapienza Univ Rome, Dept Stat, Rome, Italy
[2] Univ Roma Tor Vergata, Dept Math, Rome, Italy
来源：
JOURNAL OF THEORETICAL PROBABILITY | 2022年 / 35卷 / 04期
关键词：
Random fields; Critical points; Wiener chaos expansion; Spherical harmonics; Berry's cancellation phenomenon; CENTRAL-LIMIT-THEOREM; NODAL LENGTH; RANDOM EIGENFUNCTIONS; RANDOM WAVES; FLUCTUATIONS; INTERSECTIONS; UNIVERSALITY; VARIANCE; NUMBER;
D O I：
10.1007/s10959-021-01136-y
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We prove a Central Limit Theorem for the critical points of random spherical harmonics, in the high-energy limit. The result is a consequence of a deeper characterization of the total number of critical points, which are shown to be asymptotically fully correlated with the sample trispectrum, i.e. the integral of the fourth Hermite polynomial evaluated on the eigenfunctions themselves. As a consequence, the total number of critical points and the nodal length are fully correlated for random spherical harmonics, in the high-energy limit.
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页码：2269 / 2303
页数：35
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