A note on global suprema of band-limited spherical random functions

Domenico Marinucci and Sreekar Vadlamani

Statistics & Probability Letters, 2015, vol. 96, issue C, 141-148

Abstract: In this note, we investigate the behaviour of suprema for band-limited spherical random fields. We prove upper and lower bound for the expected values of these suprema, by means of metric entropy arguments and discrete approximations; we then exploit the Borell–TIS inequality to establish almost sure upper and lower bounds for their fluctuations. Band limited functions can be viewed as restrictions on the sphere of random polynomials with increasing degrees, and our results show that fluctuations scale as the square root of the logarithm of these degrees.

Keywords: Spherical random fields; Suprema; Metric entropy; Almost sure convergence (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2014.09.018

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