38 citations · 170 across the 22 of their papers we have counts for
22 papers · 1 filter
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…
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 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…
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…
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…
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…
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…
Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces
Valentina Cammarota, Enzo Orsingher
A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincaré half-plane and Poincaré disk) is examined. Each particle can sp…
Hitting spheres on hyperbolic spaces
Valentina Cammarota, Enzo Orsingher
For a hyperbolic Brownian motion on the Poincaré half-plane , starting from a point of hyperbolic coordinates inside a hyperbolic disc of radius $\barη…
Joint distribution of the process and its sojourn time for pseudo-processes governed by high-order heat equation
Valentina Cammarota, Aimé Lachal
Consider the high-order heat-type equation for an integer and introduce the related Markov pseudo-process $(X(t))_{t\ge…
Some Darling-Siegert relationships connected with random flights
Valentina Cammarota, Aimé Lachal, Enzo Orsingher
We derive in detail four important results on integrals of Bessel functions from which three combinatorial identities are extracted. We present the probabilistic interpretation of…