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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Spherical harmonics spherical ensemble critical radius reach curvature asymptotics large deviations

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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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