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arXiv · 2309.00437

A Useful Formula for Periodic Jacobi Matrices on Trees

Jess Banks·Jonathan Breuer·Jorge Garza Vargas·Eyal Seelig·Barry Simon
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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.

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Jess Banks, Jonathan Breuer, Jorge Garza Vargas, Eyal Seelig, Barry Simon. 2023-09-01. A Useful Formula for Periodic Jacobi Matrices on Trees. https://arxiv.org/abs/2309.00437

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