随机球谐波的临界点与临界值的相关性

IF 0.4 Q4 STATISTICS & PROBABILITY Theory of Probability and Mathematical Statistics Pub Date : 2021-07-31 DOI:10.1090/tpms/1164
Valentina Cammarota, Anna Todino
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引用次数: 0

摘要

我们研究了随机球谐的临界点总数与任意区间I⊂R I\subet \mathbb{R}中有值的临界点数量之间的相关性。我们证明了相关是渐近零的,而偏相关在控制了本征函数球面上的随机L2L^2-范数后,是渐近一的。我们的发现补充了Wigman(2012)、Marinucci和Rossi(2021)关于随机球面谐波的节点长度和边界长度之间相关性的结果。
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On the correlation between critical points and critical values for random spherical harmonics
We study the correlation between the total number of critical points of random spherical harmonics and the number of critical points with value in any interval I ⊂ R I \subset \mathbb {R} . We show that the correlation is asymptotically zero, while the partial correlation, after controlling the random L 2 L^2 -norm on the sphere of the eigenfunctions, is asymptotically one. Our findings complement the results obtained by Wigman (2012) and Marinucci and Rossi (2021) on the correlation between nodal and boundary length of random spherical harmonics.
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CiteScore
1.30
自引率
0.00%
发文量
22
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