On Nonlinear Functionals of Random Spherical Eigenfunctions
Authors:
- Domenico MarinucciDMDomenico Marinucci
- Igor WigmanIWIgor Wigman
Preprint
Abstract
We prove Central Limit Theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combine asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and Total Variation bounds for Gaussian subordinated fields. We discuss application to geometric functionals like the Defect and invariant statistics, e.g. polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.Keywords
All Related Versions
This publication has 16 references indexed in Scilit:
- The full squeezed CMB bispectrum from inflationJournal of Cosmology and Astroparticle Physics, 2012
- An estimator for statistical anisotropy from the CMB bispectrumJournal of Cosmology and Astroparticle Physics, 2012
- On the area of excursion sets of spherical Gaussian eigenfunctionsJournal of Mathematical Physics, 2011
- The defect variance of random spherical harmonicsJournal of Physics A: Mathematical and Theoretical, 2011
- Wiener Chaos: Moments, Cumulants and Diagrams2011
- Fluctuations of the Nodal Length of Random Spherical HarmonicsCommunications in Mathematical Physics, 2010
- A central limit theorem and higher order results for the angular bispectrumProbability Theory and Related Fields, 2007
- Gaussian Limits for Vector-valued Multiple Stochastic Integrals2004
- Random complex zeroes, I. Asymptotic normalityIsrael Journal of Mathematics, 2004
- Regular and irregular semiclassical wavefunctionsJournal of Physics A: General Physics, 1977