Domenico Marinucci
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Domenico Marinucci has a total of 831 co-authors. Here are the top co-authors by number of shared publications:
- Michele Liguori
Dipartimento di Fisica e Astronomia “G. Galilei”, Università degli Studi di Padova, via Marzolo 8, I-35131, Padova, Italy
15 shared publications - Sabino Matarrese
Università degli Studi di Padova
15 shared publications F. K. Hansen
11 shared publicationsD. Pietrobon
10 shared publications- Igor Wigman
Department of Mathematics, King’s College London, London, UK
10 shared publications N. Vittorio
Dipartimento di Fisica, Università di Roma Tor Vergata, via della Ricerca Scientifica 1, 00133 Roma, Italy
10 shared publications
Latest Publications
- Open Access
Sparsity for isotropic spherical random fields
We introduce a simple representation for isotropic spherical random fields and we discuss how it allows to discuss different notions of sparsity under isotropy. We also show how a suitable construction of sparse fields can mimic well the angular power spectrum and the polyspectra of some popular non-Gaussian fields, at the same time allowing for computationally efficient simulation algorithms. Using related ideas we also show how it is possible to obtain sparse approximations of spherical random fields which preserve isotropy, thus addressing an issue which has been raised in the Cosmological literature.
Open AccessSparsity for isotropic spherical random fields
We introduce a simple representation for isotropic spherical random fields and we discuss how it allows to discuss different notions of sparsity under isotropy. We also show how a suitable construction of sparse fields can mimic well the angular power spectrum and the polyspectra of some popular non-Gaussian fields, at the same time allowing for computationally efficient simulation algorithms. Using related ideas we also show how it is possible to obtain sparse approximations of spherical random fields which preserve isotropy, thus addressing an issue which has been raised in the Cosmological literature.
- Open Access
Universal Cancellations in Uniform Random Waves
A vast literature over the past fifteen years has been devoted to the study of the geometric properties of Gaussian random waves. In this work, we investigate the geometric behavior of \emph{uniform random waves}, a much less studied non-Gaussian model in which the $L^2$ norm is constrained to be exactly equal to one in every realization (a normalization that is natural from the standpoint of quantum mechanics). We show that this norm-constrained formulation has deep consequences for the universality of the so-called \emph{Berry's cancellation phenomenon}, as well as for novel high-frequency asymptotic variance estimates. These effects manifest themselves in both local geometric functionals, such as the Lipschitz--Killing curvatures, and global ones, such as the number of connected components above a fixed threshold. A key byproduct of our analysis is a new explicit relation between Hermite expansions and spherical harmonic decompositions for $0$-homogeneous functionals of Gaussian vectors, which enables a systematic chaos-based analysis of non-Gaussian random waves.Open AccessUniversal Cancellations in Uniform Random Waves
A vast literature over the past fifteen years has been devoted to the study of the geometric properties of Gaussian random waves. In this work, we investigate the geometric behavior of \emph{uniform random waves}, a much less studied non-Gaussian model in which the $L^2$ norm is constrained to be exactly equal to one in every realization (a normalization that is natural from the standpoint of quantum mechanics). We show that this norm-constrained formulation has deep consequences for the universality of the so-called \emph{Berry's cancellation phenomenon}, as well as for novel high-frequency asymptotic variance estimates. These effects manifest themselves in both local geometric functionals, such as the Lipschitz--Killing curvatures, and global ones, such as the number of connected components above a fixed threshold. A key byproduct of our analysis is a new explicit relation between Hermite expansions and spherical harmonic decompositions for $0$-homogeneous functionals of Gaussian vectors, which enables a systematic chaos-based analysis of non-Gaussian random waves. - Open Access
Fractional Cointegration of Geometric Functionals
In this paper, we show that geometric functionals (e.g., excursion area, boundary length) evaluated on excursion sets of sphere-cross-time long memory random fields can exhibit fractional cointegration, meaning that some of their linear combinations have shorter memory than the original vector. These results prove the existence of long-run equilibrium relationships between functionals evaluated at different threshold values; as a statistical application, we discuss a frequency-domain estimator for the Adler-Taylor metric factor, i.e., the variance of the field's gradient. Our results are illustrated also by Monte Carlo simulations.
Open AccessFractional Cointegration of Geometric Functionals
In this paper, we show that geometric functionals (e.g., excursion area, boundary length) evaluated on excursion sets of sphere-cross-time long memory random fields can exhibit fractional cointegration, meaning that some of their linear combinations have shorter memory than the original vector. These results prove the existence of long-run equilibrium relationships between functionals evaluated at different threshold values; as a statistical application, we discuss a frequency-domain estimator for the Adler-Taylor metric factor, i.e., the variance of the field's gradient. Our results are illustrated also by Monte Carlo simulations.
- 21 March 2025
- Published by Springer Nature in Analysis and Mathematical Physics
- Vol. 15 (2) , 1-70
Geometry and topology of spin random fields
- 21 March 2025
- Published by Springer Nature in Analysis and Mathematical Physics
- Vol. 15 (2) , 1-70
Geometry and topology of spin random fields
- Top Cited Papers
- 4 February 2025
- Published by Springer Nature in Probability Theory and Related Fields
- Vol. 191 (3-4) , 933-977
Quantitative CLTs in deep neural networks
- 4 February 2025
- Published by Springer Nature in Probability Theory and Related Fields
- Vol. 191 (3-4) , 933-977
Top Cited PapersQuantitative CLTs in deep neural networks
- Open Access
- 22 April 2024
- Published by Annual Reviews in Annual Review of Statistics and Its Application
- Vol. 11 (1) , 437-460
Geometric Methods for Cosmological Data on the Sphere
This review is devoted to recent developments in the statistical analysis of spherical data, strongly motivated by applications in cosmology. We start from a brief discussion of cosmological questions and motivations, arguing that most cosmological observables are spherical random fields. Then, we introduce some mathematical background on spherical random fields, including spectral representations and the construction of needlet and wavelet frames. We then focus on some specific issues, including tools and algorithms for map reconstruction (i.e., separating the different physical components that contribute to the observed field), geometric tools for testing the assumptions of Gaussianity and isotropy, and multiple testing methods to detect contamination in the field due to point sources. Although these tools are introduced in the cosmological context, they can be applied to other situations dealing with spherical data. Finally, we discuss more recent and challenging issues, such as the analysis of polarization data, which can be viewed as realizations of random fields taking values in spin fiber bundles.
- 22 April 2024
- Published by Annual Reviews in Annual Review of Statistics and Its Application
- Vol. 11 (1) , 437-460
Open AccessGeometric Methods for Cosmological Data on the Sphere
This review is devoted to recent developments in the statistical analysis of spherical data, strongly motivated by applications in cosmology. We start from a brief discussion of cosmological questions and motivations, arguing that most cosmological observables are spherical random fields. Then, we introduce some mathematical background on spherical random fields, including spectral representations and the construction of needlet and wavelet frames. We then focus on some specific issues, including tools and algorithms for map reconstruction (i.e., separating the different physical components that contribute to the observed field), geometric tools for testing the assumptions of Gaussianity and isotropy, and multiple testing methods to detect contamination in the field due to point sources. Although these tools are introduced in the cosmological context, they can be applied to other situations dealing with spherical data. Finally, we discuss more recent and challenging issues, such as the analysis of polarization data, which can be viewed as realizations of random fields taking values in spin fiber bundles.
- Open Access
- 1 January 2024
- Published by Institute of Mathematical Statistics in Electronic Journal of Probability
- Vol. 29 (none) , 1-27
Spherical Poisson waves
We introduce a model of Poisson random waves in S2 and we study Quantitative Central Limit Theorems when both the rate of the Poisson process and the energy (i.e., frequency) of the waves (eigenfunctions) diverge to infinity. We consider finite-dimensional distributions, harmonic coefficients and convergence in law in functional spaces, and we investigate carefully the interplay between the rate of divergence of eigenvalues and Poisson governing measures.
- 1 January 2024
- Published by Institute of Mathematical Statistics in Electronic Journal of Probability
- Vol. 29 (none) , 1-27
Open AccessSpherical Poisson waves
We introduce a model of Poisson random waves in S2 and we study Quantitative Central Limit Theorems when both the rate of the Poisson process and the energy (i.e., frequency) of the waves (eigenfunctions) diverge to infinity. We consider finite-dimensional distributions, harmonic coefficients and convergence in law in functional spaces, and we investigate carefully the interplay between the rate of divergence of eigenvalues and Poisson governing measures.
- Open Access
- 28 November 2023
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 11 (1) , 85-108
A quantitative functional central limit theorem for shallow neural networks
We prove a quantitative functional central limit theorem for one-hidden-layer neural networks with generic activation function. Our rates of convergence depend heavily on the smoothness of the activation function, and they range from logarithmic for nondifferentiable nonlinearities such as the ReLu to $\sqrt{n}$ for highly regular activations. Our main tools are based on functional versions of the Stein–Malliavin method; in particular, we rely on a quantitative functional central limit theorem which has been recently established by Bourguin and Campese [Electron. J. Probab. 25 (2020), 150].- 28 November 2023
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 11 (1) , 85-108
Open AccessA quantitative functional central limit theorem for shallow neural networks
We prove a quantitative functional central limit theorem for one-hidden-layer neural networks with generic activation function. Our rates of convergence depend heavily on the smoothness of the activation function, and they range from logarithmic for nondifferentiable nonlinearities such as the ReLu to $\sqrt{n}$ for highly regular activations. Our main tools are based on functional versions of the Stein–Malliavin method; in particular, we rely on a quantitative functional central limit theorem which has been recently established by Bourguin and Campese [Electron. J. Probab. 25 (2020), 150]. - Open AccessMinkowski Functionals in $SO(3)$ for the spin-2 CMB polarisation fieldThe study of the angular power spectrum of Cosmic Microwave Background (CMB) anisotropies, both in intensity and in polarisation, has led to the tightest constraints on cosmological parameters. However, this statistical quantity is not sensitive to any deviation from Gaussianity and statistical isotropy in the CMB data. Minkowski Functionals (MFs) have been adopted as one of the most powerful statistical tools to study such deviations, since they characterise the topology and geometry of the field of interest. In this paper, we extend the application of MFs to CMB polarisation data by introducing a new formalism, where we lift the spin $2$ polarisation field to a scalar function in a higher-dimensional manifold: the group of rotations of the sphere, $SO(3)$. Such a function is defined as $f = Q \cos(2ψ) - U \sin(2ψ)$. We analytically obtain the expected values for the MFs of $f$ in the case of Gaussian isotropic polarisation maps. Furthermore, we present a new pipeline which estimates these MFs from input HEALPix polarisation maps. We apply it to CMB simulations in order to validate the theoretical results and the methodology. The pipeline is to be included in the publicly available Python package $\texttt{Pynkowski}$ available at https://github.com/javicarron/pynkowski.Open AccessMinkowski Functionals in $SO(3)$ for the spin-2 CMB polarisation fieldThe study of the angular power spectrum of Cosmic Microwave Background (CMB) anisotropies, both in intensity and in polarisation, has led to the tightest constraints on cosmological parameters. However, this statistical quantity is not sensitive to any deviation from Gaussianity and statistical isotropy in the CMB data. Minkowski Functionals (MFs) have been adopted as one of the most powerful statistical tools to study such deviations, since they characterise the topology and geometry of the field of interest. In this paper, we extend the application of MFs to CMB polarisation data by introducing a new formalism, where we lift the spin $2$ polarisation field to a scalar function in a higher-dimensional manifold: the group of rotations of the sphere, $SO(3)$. Such a function is defined as $f = Q \cos(2ψ) - U \sin(2ψ)$. We analytically obtain the expected values for the MFs of $f$ in the case of Gaussian isotropic polarisation maps. Furthermore, we present a new pipeline which estimates these MFs from input HEALPix polarisation maps. We apply it to CMB simulations in order to validate the theoretical results and the methodology. The pipeline is to be included in the publicly available Python package $\texttt{Pynkowski}$ available at https://github.com/javicarron/pynkowski.
- Open Access
Some Recent Developments on the Geometry of Random Spherical Eigenfunctions
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 harmonics, i.e., Gaussian eigenfunctions for the spherical Laplacian $\Delta_{\mathbf{S}^2}$. In this survey we shall review some of these results, with particular reference to the asymptotic behaviour of variances, phase transitions in the nodal case (the \emph{Berry's Cancellation Phenomenon}), the distribution of the fluctuations around the expected values, and the asymptotic correlation among different functionals. We shall also discuss some connections with the Gaussian Kinematic Formula, with Wiener-Chaos expansions and with recent developments in the derivation of Quantitative Central Limit Theorems (the so-called Stein-Malliavin approach).Open AccessSome Recent Developments on the Geometry of Random Spherical Eigenfunctions
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 harmonics, i.e., Gaussian eigenfunctions for the spherical Laplacian $\Delta_{\mathbf{S}^2}$. In this survey we shall review some of these results, with particular reference to the asymptotic behaviour of variances, phase transitions in the nodal case (the \emph{Berry's Cancellation Phenomenon}), the distribution of the fluctuations around the expected values, and the asymptotic correlation among different functionals. We shall also discuss some connections with the Gaussian Kinematic Formula, with Wiener-Chaos expansions and with recent developments in the derivation of Quantitative Central Limit Theorems (the so-called Stein-Malliavin approach).