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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.AG2025
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…
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…