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20182026
most citedGeneric Laplace eigenfunctions on metric graphs

2 citations · 3 across the 8 of their papers we have counts for

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6 papers · 1 filter

math-ph2025

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…

math-ph2025

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…

math-ph2024

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…

math-ph2024

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…

math-ph20241 cited

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…

math-ph2020

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…