Publications de Riccardo Walter Maffucci

ON THE LIMITING BEHAVIOUR OF ARITHMETIC TORAL EIGENFUNCTIONS

Alejandro Rivera, Riccardo Walter Maffucci

We consider a wide class of families (Fm)m is an element of N of Gaussian fields on 1Cd = Rd/Zd defined by Fm : x-* 1 _ X p|Am| l lambda ei2 pi lambda is an element of Lambda m where the l lambda's are independent standard normals and Am is the ...

ANNALES INST FOURIER2025

On Unigraphic Polyhedra with One Vertexof Degreep-2

Riccardo Walter Maffucci

A sequence sigma of p non-negative integers is unigraphic if it is the degree sequence of exactly one graph, up to isomorphism. A polyhedral graph is a 3-connected, planar graph. We investigate which sequences are unigraphic with respect to the class of po ...

Springer Basel Ag2024

Independence numbers of polyhedral graphs

Riccardo Walter Maffucci

A polyhedral graph is a 3-connected planar graph. We find the least possible order p(k, a) of a polyhedral graph containing a k-independent set of size a for all positive integers k and a. In the case k =1 and a even, we prove that the extremal graphs are ...

Elsevier Science Inc2023

On polyhedral graphs and their complements

Riccardo Walter Maffucci

We find all polyhedral graphs such that their complements are still polyhedral. These turn out to be all self-complementary. ...

2022

Intermediate and small scale limiting theorems for random fields

Riccardo Walter 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 intersections of the nodal line with a straight interval in a given direction. We ar ...

2022

Restriction of 3D arithmetic Laplace eigenfunctions to a plane

Riccardo Walter Maffucci

We consider a random Gaussian ensemble of Laplace eigenfunctions on the 3D torus, and investigate the 1-dimensional Hausdorff measure ('length') of nodal intersections against a smooth 2-dimensional toral sub-manifold ('surface'). A prior result of ours pr ...

2020