Asymptotic Behaviour of Level Sets of Needlet Random Fields

2020/11/05 by Radomyra Shevchenko, Shevchenko, Radomyra, Anna Paola Todino +1 · 1 citation
Mathematics · Computer Science · #Geometry and complex manifolds #Stochastic processes and statistical mechanics #Data Management and Algorithms

paper · pdf · doi:10.48550/arxiv.2011.02856

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 Stein-Malliavin techniques and Wiener chaos expansion 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.

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• Scale Dilation Dynamics in Flexible Bandwidth Needlet Constructions

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