Critical radius and supremum of random spherical harmonics (II)

被引：2
|
作者：
Feng, Renjie [1 ]
Xu, Xingcheng [2 ]
Adler, Robert J. [3 ]
机构：
[1] Peking Univ, Beijing Int Ctr Math Res, Beijing, Peoples R China
[2] Peking Univ, Sch Math Sci, Beijing, Peoples R China
[3] Technion Israel Inst Technol, Andrew & Erna Viterbi Fac Elect Engn, IL-32000 Haifa, Israel
来源：
ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2018年 / 23卷
关键词：
Spherical harmonics; spherical ensemble; critical radius; reach; curvature; asymptotics; large deviations; GAUSSIAN RANDOM-FIELDS;
D O I：
10.1214/18-ECP156
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 continue the study, begun in [6], of the critical radius of embeddings, via deterministic spherical harmonics, of fixed dimensional spheres into higher dimensional ones, along with the associated problem of the distribution of the suprema of random spherical harmonics. Whereas [6] concentrated on spherical harmonics of a common degree, here we extend the results to mixed degrees, en passant improving on the lower bounds on critical radii that we found previously.
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页数：11
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