8 papers · 1 filter
New chaos decomposition of Gaussian nodal volumes
Michele Stecconi, Anna Paola Todino
We investigate the random variable defined by the volume of the zero set of a smooth Gaussian field, on a general Riemannian manifold possibly with boundary, a fundamental object i…
Flexible-bandwidth Needlets
Claudio Durastanti, Domenico Marinucci, Anna Paola Todino
We investigate here a generalized construction of spherical wavelets/needlets which admits extra-flexibility in the harmonic domain, i.e., it allows the corresponding support in mu…
On the correlation between critical points and critical values for random spherical harmonics
Valentina Cammarota, Anna Paola Todino
We study the correlation between the total number of critical points of random spherical harmonics and the number of critical points with value in any interval $I \subset \mathbb{R…
Asymptotic Behaviour of Level Sets of Needlet Random Fields
Radomyra Shevchenko, Anna Paola Todino
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 energ…
Moderate Deviation estimates for Nodal Lengths of Random Spherical Harmonics
Claudio Macci, Maurizia Rossi, Anna Paola Todino
We prove Moderate Deviation estimates for nodal lengths of random spherical harmonics both on the whole sphere and on shrinking spherical domains. Central Limit Theorems for the la…
Limiting Behavior for the Excursion Area of Band-Limited Spherical Random Fields
Anna Paola Todino
In this paper, we investigate some geometric functionals for band limited Gaussian and isotropic spherical random fields in dimension 2. In particular, we focus on the area of excu…