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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…
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 limiting behaviour of arithmetic toral eigenfunctions
Riccardo W. Maffucci, Alejandro Rivera
We consider a wide class of families of Gaussian fields on defined by \[F_m:x\mapsto \frac{1}{\sqrt{|Λ_m|}}\sum_{λ…
Coupling of stationary fields with application to arithmetic waves
Dmitry Beliaev, Riccardo W. Maffucci
In this paper we obtain a range of quantitative results of the following type: given two centered Gaussian fields with close covariance kernels we construct a coupling such that th…
Intermediate and small scale limiting theorems for random fields
Dmitry Beliaev, Riccardo W. Maffucci
In this paper we study the nodal lines of random eigenfunctions of the Laplacian on the torus, the so called 'arithmetic waves'. To be more precise, we study the number of intersec…