Electronic Communications in Probability

Critical radius and supremum of random spherical harmonics (II)

Renjie Feng, Xingcheng Xu, and Robert J. Adler

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Abstract

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.

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 50, 11 pp.

Dates
Received: 26 September 2017
Accepted: 24 July 2018
First available in Project Euclid: 1 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1535767261

Digital Object Identifier
doi:10.1214/18-ECP156

Mathematical Reviews number (MathSciNet)
MR3852264

Zentralblatt MATH identifier
1401.60057

Subjects
Primary: 33C55: Spherical harmonics 60G15: Gaussian processes
Secondary: 60F10: Large deviations 60G60: Random fields

Keywords
Spherical harmonics spherical ensemble critical radius reach curvature asymptotics large deviations

Rights
Creative Commons Attribution 4.0 International License.

Citation

Feng, Renjie; Xu, Xingcheng; Adler, Robert J. Critical radius and supremum of random spherical harmonics (II). Electron. Commun. Probab. 23 (2018), paper no. 50, 11 pp. doi:10.1214/18-ECP156. https://projecteuclid.org/euclid.ecp/1535767261


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References

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