The defect variance of random spherical harmonics

Wigman, Igor and Marinucci, Domenico 2011. The defect variance of random spherical harmonics. Journal of Physics A: Mathematical and Theoretical 44 (35) , 355206. 10.1088/1751-8113/44/35/355206

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Abstract

The defect of a function [IMAGE] is defined as the difference between the measure of the positive and negative regions. In this paper, we begin the analysis of the distribution of defect of random Gaussian spherical harmonics. By an easy argument, the defect is non-trivial only for even degree and the expected value always vanishes. Our principal result is evaluating the defect variance, asymptotically in the high-frequency limit. As other geometric functionals of random eigenfunctions, the defect may be used as a tool to probe the statistical properties of spherical random fields, a topic of great interest for modern cosmological data analysis.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	IOP Publishing
ISSN:	0160-6999
Last Modified:	26 Jun 2019 01:57
URI:	https://orca.cardiff.ac.uk/id/eprint/17717

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