2 citations · 3 across the 8 of their papers we have counts for
6 papers · 1 filter
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…
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…
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…