457 citations · 2.3k across the 77 of their papers we have counts for
32 papers · 1 filter
A Quantitative Functional Central Limit Theorem for Shallow Neural Networks
Valentina Cammarota, Domenico Marinucci, Michele Salvi +1
We prove a Quantitative Functional Central Limit Theorem for one-hidden-layer neural networks with generic activation function. The rates of convergence that we establish depend he…
Fluctuations of Level Curves for Time-Dependent Spherical Random Fields
Domenico Marinucci, Maurizia Rossi, Anna Vidotto
The investigation of the behaviour for geometric functionals of random fields on manifolds has drawn recently considerable attention. In this paper, we extend this framework by con…
Geometry and topology of spin random fields
Antonio Lerario, Domenico Marinucci, Maurizia Rossi +1
Spin (spherical) random fields are very important in many physical applications, in particular they play a key role in Cosmology, especially in connection with the analysis of the…
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…
Some Recent Developments on the Geometry of Random Spherical Eigenfunctions
Domenico Marinucci
A lot of efforts have been devoted in the last decade to the investigation of the high-frequency behaviour of geometric functionals for the excursion sets of random spherical harmo…
Lipschitz-Killing Curvatures for Arithmetic Random Waves
Valentina Cammarota, Domenico Marinucci, Maurizia Rossi
In this paper, we show that the Lipschitz-Killing Curvatures for the excursion sets of Arithmetic Random Waves (toral Gaussian eigenfunctions) are dominated, in the high-frequency…
Non-Universal Fluctuations of the Empirical Measure for Isotropic Stationary Fields on
Domenico Marinucci, Maurizia Rossi, Anna Vidotto
In this paper, we consider isotropic and stationary real Gaussian random fields defined on and we investigate the asymptotic behavior, as $T\rightarr…
On the Correlation of Critical Points and Angular Trispectrum for Random Spherical Harmonics
Valentina Cammarota, Domenico Marinucci
We prove a Central Limit Theorem for the Critical Points of Random Spherical Harmonics, in the High-Energy Limit. The result is a consequence of a deeper characterizations of the t…
A Reduction Principle for the Critical Values of Random Spherical Harmonics
Valentina Cammarota, Domenico Marinucci
We study here the random fluctuations in the number of critical points with values in an interval for Gaussian spherical eigenfunctions $\left\{f_{\ell }\righ…
The Asymptotic Equivalence of the Sample Trispectrum and the Nodal Length for Random Spherical Harmonics
Domenico Marinucci, Maurizia Rossi, Igor Wigman
We study the asymptotic behaviour of the nodal length of random -spherical harmonics of high degree , i.e. the length of their zero set $f_{\…
A Quantitative Central Limit Theorem for the Euler-Poincaré Characteristic of Random Spherical Eigenfunctions
Valentina Cammarota, Domenico Marinucci
We establish here a Quantitative Central Limit Theorem (in Wasserstein distance) for the Euler-Poincaré Characteristic of excursion sets of random spherical eigenfunctions in dimen…
Strong Local Nondeterminism and Exact Modulus of Continuity for Spherical Gaussian Fields
Xiaohong Lan, Domenico Marinucci, Yimin Xiao
In this paper, we are concerned with sample path properties of isotropic spherical Gaussian fields on . In particular, we establish the property of strong local nondeterminism…
Approximate Normality of High-Energy Hyperspherical Eigenfunctions
Simon Campese, Domenico Marinucci, Maurizia Rossi
The Berry heuristic has been a long standing \emph{ansatz} about the high energy (i.e. large eigenvalues) behaviour of eigenfunctions (see Berry 1977). Roughly speaking, it states…
Fluctuations of the Euler-Poincaré characteristic for random spherical harmonics
Valentina Cammarota, Domenico Marinucci, Igor Wigman
In this short note, we build upon some recent results to present a precise expression for the asymptotic variance of the Euler-Poincaré characteristic for the excursion sets of Gau…
Gaussian approximations of nonlinear statistics on the sphere
Solesne Bourguin, Claudio Durastanti, Domenico Marinucci +1
We show how it is possible to assess the rate of convergence in the Gaussian approximation of triangular arrays of -statistics, built from wavelets coefficients evaluated on a h…
Stein-Malliavin Approximations for Nonlinear Functionals of Random Eigenfunctions on
Domenico Marinucci, Maurizia Rossi
We investigate Stein-Malliavin approximations for nonlinear functionals of geometric interest of Gaussian random eigenfunctions on the unit -dimensional sphere ${\mathbb{S}}^{d…
A Note on Global Suprema of Band-Limited Spherical Random Functions
Domenico Marinucci, Sreekar Vadlamani
In this note, we investigate the behaviour of suprema for band-limited spherical random fields. We prove upper and lower bound for the expected values of these suprema, by means of…
The Stochastic Properties of -Regularized Spherical Gaussian Fields
Valentina Cammarota, Domenico Marinucci
Convex regularization techniques are now widespread tools for solving inverse problems in a variety of different frameworks. In some cases, the functions to be reconstructed are na…
On the Limiting Behaviour of Needlets Polyspectra
Valentina Cammarota, Domenico Marinucci
This paper provides quantitative Central Limit Theorems for nonlinear transforms of spherical random fields, in the high frequency limit. The sequences of fields that we consider a…
High-frequency asymptotics for Lipschitz-Killing curvatures of excursion sets on the sphere
Domenico Marinucci, Sreekar Vadlamani
In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields…
Mean-Square Continuity on Homogeneous Spaces of Compact Groups
Domenico Marinucci, Giovanni Peccati
We show that any finite-variance, isotropic random field on a compact group is necessarily mean-square continuous, under standard measurability assumptions. The result extends to i…
Normal Approximations for Wavelet Coefficients on Spherical Poisson Fields
Claudio Durastanti, Domenico Marinucci, Giovanni Peccati
We compute explicit upper bounds on the distance between the law of a multivariate Gaussian distribution and the joint law of wavelets/needlets coefficients based on a homogeneous…
On the Excursion Sets of Spherical Gaussian Eigenfunctions
Domenico Marinucci, Igor Wigman
The high frequency behaviour for random eigenfunctions of the spherical Laplacian has been recently the object of considerable interest, also because of strong motivations arising…