arXiv subjects
Publications and source records attributed to 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 other eigenvalue gaps.
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 and Aomoto index theorems. We prove a version of this new formula for the Anderson model on trees.
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. We complement this with the analog of the result from arXiv:1011.3159 showing that clock spacing holds even for certain singular continuous measures.