Critical radius and supremum of random spherical harmonics (II)

Renjie Feng; Xingcheng Xu; Robert J. Adler

doi:10.1214/18-ecp156

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arXiv · 1709.00691

Critical radius and supremum of random spherical harmonics (II)

Renjie Feng·Xingcheng Xu·Robert J. Adler

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Abstract

We continue the study, begun in \cite{FA}, 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 \cite{FA} concentrated on spherical harmonics of a common degree, here we extend the results to mixed degrees, obtaining larger lower bounds on critical radii than we found previously.

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Renjie Feng, Xingcheng Xu, Robert J. Adler. 2017-09-03. Critical radius and supremum of random spherical harmonics (II). https://doi.org/10.1214/18-ecp156

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