A Useful Formula for Periodic Jacobi Matrices on Trees
Spectral Theory
2023-09-04 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.2309.00437,
title = {A Useful Formula for Periodic Jacobi Matrices on Trees},
author = {Jess Banks and Jonathan Breuer and Jorge Garza Vargas and Eyal Seelig and Barry Simon},
journal= {arXiv preprint arXiv:2309.00437},
year = {2023}
}