18 citations · 29 across the 16 of their papers we have counts for
17 papers
Statistics on Yau's conjecture: Variance asymptotics
Michele Stecconi, Anna Paola Todino
We investigate the probabilistic counterpart of Yau's conjecture on the nodal volume of Laplace eigenfunctions on compact manifolds, by studying the high-frequency variance asympto…
Berry-Heisenberg Random Waves
Marco Carfagnini, Anna Paola Todino
We construct a new family of random fields on the Heisenberg group , the sub-Riemannian analog of . These fields are generalized random eigenfunctions o…
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…
On the Euler-Poincaré Characteristic of the planar Berry's random wave: fluctuations and a perturbation study
Elena Di Bernardino, Radomyra Shevchenko, Anna Paola Todino
We prove the Central Limit Theorem for the Euler-Poincaré characteristic of Berry's random wave model in a growing domain. We also show Gaussian fluctuations for a class of Berry's…
Small fluctuations for time-dependent spherical random fields
Marco Carfagnini, Anna Paola Todino
We consider time-dependent space isotropic and time stationary spherical Gaussian random fields. We establish Chung's law of the iterated logarithm and solve the small probabilitie…
Laguerre Expansion for Nodal Volumes and Applications
Domenico Marinucci, Maurizia Rossi, Anna Paola Todino
We investigate the nodal volume of random hyperspherical harmonics on the -dimensional unit sphere (). We exploit an orth…
Fluctuations of Polyspectra in Spherical and Euclidean Random Wave Models
Francesco Grotto, Leonardo Maini, Anna Paola Todino
We consider polynomial transforms (polyspectra) of Berry's model -- the Euclidean Random Wave model -- and of Random Hyperspherical Harmonics. We determine the asymptotic behavior…
No smooth Phase Transition for the Nodal Length of Band-limited Spherical Random Fields
Anna Paola Todino
In this paper, we investigate the variance of the nodal length for band-limited spherical random waves. When the frequency window includes a number of eigenfunctions that grows lin…
Spherical Poisson Waves
Solesne Bourguin, Claudio Durastanti, Domenico Marinucci +1
We introduce a model of Poisson random waves in and we study Quantitative Central Limit Theorems when both the rate of the Poisson process and the energy (i.e., fr…
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…
A Numerical Investigation on the High-Frequency Geometry of Spherical Random Eigenfunctions
Yabebal Fantaye, Valentina Cammarota, Domenico Marinucci +1
A lot of attention has been drawn over the last few years by the investigation of the geometry of spherical random eigenfunctions (random spherical harmonics) in the high frequency…
Nodal Lengths in Shrinking Domains for Random Eigenfunctions on
Anna Paola Todino
We investigate the asymptotic behavior of the nodal lines for random spherical harmonics restricted to shrinking domains, in the 2-dimensional case: i.e., the length of the zero se…
A Quantitative Central Limit Theorem for the Excursion Area of Random Spherical Harmonics over Subdomains of
Anna Paola Todino
In recent years, considerable interest has been drawn by the analysis of geometric functionals for the excursion sets of random eigenfunctions on the unit sphere (spherical harmoni…