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The defect of a function $f:M\rightarrow \mathbb{R}$ 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 obtaining the asymptotic shape of the defect variance, 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.Comment: 19 page

Topics:
Mathematical Physics, Mathematics - Probability, 60G60, 60G15, 42C10, 60D05

Year: 2011

DOI identifier: 10.1088/1751-8113/44/35/355206

OAI identifier:
oai:arXiv.org:1103.0232

Provided by:
arXiv.org e-Print Archive

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