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math.SP2024
Spectral Gaps for Jacobi Matrices on Graphs
Jonathan Breuer, Eyal Seelig
We study bounds on eigenvalue gaps for finite quotients of periodic Jacobi matrices on trees. We prove an Alon-Boppana type bound for the spectral gap and a comparison result for o…
math.SP2023
A Useful Formula for Periodic Jacobi Matrices on Trees
Jess Banks, Jonathan Breuer, Jorge Garza Vargas +2
We introduce a function of the density of states for periodic Jacobi matrices on trees and prove a useful formula for it. This allows new, streamlined proofs of the gap labeling an…
math.SP2019
On the spacing of zeros of paraorthogonal polynomials for singular measures
Jonathan Breuer, Eyal Seelig
We prove a lower bound on the spacing of zeros of paraorthogonal polynomials on the unit circle, based on continuity of the underlying measure as measured by Hausdorff dimensions.…