18 citations · 44 across the 16 of their papers we have counts for
16 papers
Wave Transport in Fourier Quasicrystals Revealed by Water Waves
Angélique Campaniello, Lior Alon, Rémi Carminati +2
Fourier quasicrystals are aperiodic structures whose diffraction spectrum consists not of a dense set of Bragg peaks, as in ordinary quasicrystals, but of isolated ones scattered a…
Nodal Count for Orthogonally Invariant Ensembles
Lior Alon, Dan Mikulincer, John Urschel
We investigate the nodal count of eigenvectors of random matrices interpreted as operators on signed complete graphs. Our focus is on orthogonally invariant ensembles, with particu…
Periodic Hypersurfaces and Lee-Yang Polynomials
Lior Alon, Mario Kummer
We study periodic measures on whose Fourier transform is confined to a proper double cone, in the sense of Meyer's notion of lighthouse measures. Lee--Yang polynomia…
Smooth critical points of eigenvalues on the torus of magnetic perturbations of graphs
Lior Alon, Gregory Berkolaiko, Mark Goresky
Motivated by the nodal distribution universality conjecture for discrete operators on graphs and by the spectral analysis of their maximal abelian covers, we consider a family of H…
Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties
Lior Alon, Mario Kummer, Pavel Kurasov +1
In this paper, we construct Fourier quasicrystals with unit masses in arbitrary dimensions. This generalizes a one-dimensional construction of Kurasov and Sarnak. To do this, we em…
Average Nodal Count and the Nodal Count Condition for Graphs
Lior Alon, John Urschel
The nodal edge count of an eigenvector of the Laplacian of a graph is the number of edges on which it changes sign. This quantity extends to any real symmetric matrix s…
Nodal count for a random signing of a graph with disjoint cycles
Lior Alon, Mark Goresky
Let be a simple, connected graph on vertices, and further assume that has disjoint cycles. Let be a real symmetric matrix supported on (for example, a discrete…
Gap distributions of Fourier quasicrystals via Lee-Yang polynomials
Lior Alon, Cynthia Vinzant
Recent work of Kurasov and Sarnak provides a method for constructing one-dimensional Fourier quasicrystals (FQ) from the torus zero sets of a special class of multivariate polynomi…
Every real-rooted exponential polynomial is the restriction of a Lee-Yang polynomial
Lior Alon, Alex Cohen, Cynthia Vinzant
A Lee-Yang polynomial is a polynomial that has no zeros in the polydisc and its inverse $ (\mathbb{C}\setminus\overline{\mathbb{D}})^{n…
Morse theory for discrete magnetic operators and nodal count distribution for graphs
Lior Alon, Mark Goresky
Given a discrete Schrödinger operator on a finite connected graph of vertices, the nodal count denotes the number of edges on which the -th eigenvector chan…
Generic Laplace eigenfunctions on metric graphs
Lior Alon
It is known that up to certain pathologies, a compact metric graph with standard vertex conditions has a Baire-generic set of choices of edge lengths such that all Laplacian eigenv…
Universality of nodal count distribution in large metric graphs
Lior Alon, Ram Band, Gregory Berkolaiko
An eigenfunction of the Laplacian on a metric (quantum) graph has an excess number of zeros due to the graph's non-trivial topology. This number, called the nodal surplus, is an in…
Quantum graphs -- Generic eigenfunctions and their nodal count and Neumann count statistics
Lior Alon
In this thesis, we study Laplacian eigenfunctions on metric graphs, also known as quantum graphs. We restrict the discussion to standard quantum graphs. These are finite connected…
Neumann Domains on Quantum Graphs
Lior Alon, Ram Band
The Neumann points of an eigenfunction on a quantum (metric) graph are the interior zeros of . The Neumann domains of are the sub-graphs bounded by the Neumann points.…
Neumann Domains on Graphs and Manifolds
Lior Alon, Ram Band, Michael Bersudsky +1
The nodal set of a Laplacian eigenfunction forms a partition of the underlying manifold or graph. Another natural partition is based on the gradient vector field of the eigenfuncti…
Nodal Statistics On Quantum Graphs
Lior Alon, Ram Band, Gregory Berkolaiko
It has been suggested that the distribution of the suitably normalized number of zeros of Laplacian eigenfunctions contains information about the geometry of the underlying domain.…