31 citations · 111 across the 26 of their papers we have counts for
33 papers
Almost sure central limit theorems via chaos expansions and related results
Leonardo Maini, Maurizia Rossi, Guangqu Zheng
In this work, we investigate the asymptotic behavior of integral functionals of stationary Gaussian random fields as the integration domain tends to be the whole space. More precis…
Sojourn functionals of time-dependent -random fields on two-point homogeneous spaces
Alessia Caponera, Maurizia Rossi, María Dolores Ruiz Medina
In this note we investigate geometric properties of invariant spatio-temporal random fields defined on a compact two-point homogeneous…
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…
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…
Quasi-critical fluctuations for 2d directed polymers
Francesco Caravenna, Francesca Cottini, Maurizia Rossi
We study the 2d directed polymer in random environment in a novel *quasi-critical regime*, which interpolates between the much studied sub-critical and critical regimes. We prove E…
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…
Non-Universal Moderate Deviation Principle for the Nodal Length of Arithmetic Random Waves
Claudio Macci, Maurizia Rossi, Anna Vidotto
Inspired by the recent work [MRT21], we prove a non-universal non-central Moderate Deviation principle for the nodal length of arithmetic random waves (Gaussian Laplace eigenfuncti…
Convergence in Total Variation for nonlinear functionals of random hyperspherical harmonics
Lucia Caramellino, Giacomo Giorgio, Maurizia Rossi
Random hyperspherical harmonics are Gaussian Laplace eigenfunctions on the unit -dimensional sphere (). We study the convergence in Total Variation distance for their no…
Asymptotic distribution of Nodal Intersections for ARW against a Surface
Riccardo W. Maffucci, Maurizia Rossi
We investigate Gaussian Laplacian eigenfunctions (Arithmetic Random Waves) on the three-dimensional standard flat torus, in particular the asymptotic distribution of the nodal inte…
On the equivalence of Sobolev norms in Malliavin spaces
Davide Addona, Matteo Muratori, Maurizia Rossi
We investigate the problem of the equivalence of -Sobolev norms in Malliavin spaces for , focusing on the graph norm of the -th Malliavin derivative operat…
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…
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…
Small Scale CLTs for the Nodal Length of Monochromatic Waves
Gauthier Dierickx, Ivan Nourdin, Giovanni Peccati +1
We consider the nodal length of the restriction to a ball of radius of a {\it Gaussian pullback monochromatic random wave} of parameter associated with a Riemann…
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 excursion area of perturbed Gaussian fields
Elena Di Bernardino, Anne Estrade, Maurizia Rossi
We investigate Lipschitz-Killing curvatures for excursion sets of random fields on under small spatial-invariant random perturbations. An expansion formula for mean c…
On the correlation between nodal and boundary lengths for random spherical harmonics
Domenico Marinucci, Maurizia Rossi
We study the correlation between the nodal length of random spherical harmonics and the measure of the boundary for excursion sets at any non-zero level. We show that the correlati…
Random Nodal Lengths and Wiener Chaos
Maurizia Rossi
In this survey we collect some of the recent results on the "nodal geometry" of random eigenfunctions on Riemannian surfaces. We focus on the asymptotic behavior, for high energy l…
Nodal Statistics of Planar Random Waves
Ivan Nourdin, Giovanni Peccati, Maurizia Rossi
We consider Berry's random planar wave model (1977) for a positive Laplace eigenvalue , both in the real and complex case, and prove limit theorems for the nodal statistics as…
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_{\…
Quantitative limit theorems for local functionals of arithmetic random waves
Giovanni Peccati, Maurizia Rossi
We consider Gaussian Laplace eigenfunctions on the two-dimensional flat torus (arithmetic random waves), and provide explicit Berry-Esseen bounds in the 1-Wasserstein distance for…
Asymptotic distribution of nodal intersections for arithmetic random waves
Maurizia Rossi, Igor Wigman
We study the nodal intersections number of random Gaussian toral Laplace eigenfunctions ("arithmetic random waves") against a fixed smooth reference curve. The expected intersectio…
Phase Singularities in Complex Arithmetic Random Waves
Federico Dalmao, Ivan Nourdin, Giovanni Peccati +1
Complex arithmetic random waves are stationary Gaussian complex-valued solutions of the Helmholtz equation on the two-dimensional flat torus. We use Wiener-Itô chaotic expansions i…
The Defect of Random Hyperspherical Harmonics
Maurizia Rossi
Random hyperspherical harmonics are Gaussian Laplace eigenfunctions on the unit -sphere (). We investigate the distribution of their defect i.e., the difference between…