Asymptotic behaviour of level sets of needlet random fields

Radomyra Shevchenko and Anna Paola Todino

Stochastic Processes and their Applications, 2023, vol. 155, issue C, 268-318

Abstract: We consider sequences of needlet random fields defined as weighted averaged forms of spherical Gaussian eigenfunctions. Our main result is a Central Limit Theorem in the high energy setting, for the boundary lengths of their excursion sets. This result is based on Wiener chaos expansion and Stein–Malliavin techniques for nonlinear functionals of random fields. To this end, a careful analysis of the variances of each chaotic component of the boundary length is carried out, showing that they are asymptotically constant, after normalisation, for all terms of the expansion and no leading component arises.

Keywords: Gaussian spherical eigenfunctions; Spherical needlets; Boundary length; Wiener chaos; Excursion sets; Central limit theorem (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2022.10.011

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