38 citations · 170 across the 22 of their papers we have counts for
28 papers
Correlation Structure and Resonant Pairs for Arithmetic Random Waves
Valentina Cammarota, Riccardo-W. Maffucci, Domenico Marinucci +1
The geometry of Arithmetic Random Waves has been extensively investigated in the last fifteen years, starting from the seminal papers [RW08, ORW08]. In this paper we study the corr…
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…
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…
Nodal deficiency of random spherical harmonics in presence of boundary
Valentina Cammarota, Domenico Marinucci, Igor Wigman
We consider a random Gaussian model of Laplace eigenfunctions on the hemisphere satisfying the Dirichlet boundary conditions along the equator. For this model we find a precise asy…
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…
No repulsion between critical points for planar Gaussian random fields
Dmitry Beliaev, Valentina Cammarota, Igor Wigman
We study the behaviour of the point process of critical points of isotropic stationary Gaussian fields. We compute the main term in the asymptotic expansion of the two-point correl…
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…
Boundary effect on the nodal length for Arithmetic Random Waves, and spectral semi-correlations
Valentina Cammarota, Oleksiy Klurman, Igor Wigman
We test M. Berry's ansatz on nodal deficiency in presence of boundary. The square billiard is studied, where the high spectral degeneracies allow for the introduction of a Gaussian…
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…
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…
Nodal area distribution for arithmetic random waves
Valentina Cammarota
We obtain the limiting distribution of the nodal area of random Gaussian Laplace eigenfunctions on (-dimensional 'arithmetic random wa…
Two point function for critical points of a random plane wave
Dmitry Beliaev, Valentina Cammarota, Igor Wigman
Random plane wave is conjectured to be a universal model for high-energy eigenfunctions of the Laplace operator on generic compact Riemanian manifolds. This is known to be true on…
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…
Multiple testing of local maxima for detection of peaks on the (celestial) sphere
Dan Cheng, Valentina Cammarota, Yabebal Fantaye +2
We present a topological multiple testing scheme for detecting peaks on the sphere under isotropic Gaussian noise, where tests are performed at local maxima of the observed field f…
Fluctuations of the total number of critical points of random spherical harmonics
Valentina Cammarota, Igor Wigman
We determine the asymptotic law for the fluctuations of the total number of critical points of random Gaussian spherical harmonics in the high degree limit. Our results have implic…
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…
Entrance and sojourn times for Markov chains. Application to -random walks
Valentina Cammarota, Aimé Lachal
In this paper, we provide a methodology for computing the probability distribution of sojourn times for a wide class of Markov chains. Our methodology consists in writing out linea…
On the distribution of the critical values of random spherical harmonics
Valentina Cammarota, Domenico Marinucci, Igor Wigman
We study the limiting distribution of critical points and extrema of random spherical harmonics, in the high energy limit. In particular, we first derive the density functions of e…
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…
Sparse Inpainting and Isotropy
Stephen M. Feeney, Domenico Marinucci, Jason D. McEwen +3
Sparse inpainting techniques are gaining in popularity as a tool for cosmological data analysis, in particular for handling data which present masked regions and missing observatio…
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…
On the asymptotic behavior of the hyperbolic Brownian motion
Valentina Cammarota, Alessandro De Gregorio, Claudio Macci
The main results in this paper concern large and moderate deviations for the radial component of a -dimensional hyperbolic Brownian motion (for ) on the Poincaré half-s…
On the most visited sites of planar Brownian motion
Valentina Cammarota, Peter Mörters
Let (B_t : t > 0) be a planar Brownian motion and define gauge functions for . If we show that almost surely there exists a point x in the plane s…
Travelling Randomly on the Poincaré Half-Plane with a Pythagorean Compass
Valentina Cammarota, Enzo Orsingher
A random motion on the Poincaré half-plane is studied. A particle runs on the geodesic lines changing direction at Poisson-paced times. The hyperbolic distance is analyzed, also in…