A Useful Formula for Periodic Jacobi Matrices on Trees
Jess Banks, Jonathan Breuer, Jorge Garza Vargas, Eyal Seelig, Barry, Simon
TL;DR
This paper introduces a density of states function for periodic Jacobi matrices on trees, providing a new formula that simplifies proofs of key theorems and extends to the Anderson model on trees.
Contribution
It presents a novel formula for the density of states in periodic Jacobi matrices on trees, enabling streamlined proofs and extensions to the Anderson model.
Findings
New formula for the density of states on trees
Simplified proofs of gap labeling and Aomoto index theorems
Extension of the formula to the Anderson model on trees
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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Taxonomy
TopicsGraph theory and applications · Topological and Geometric Data Analysis · Spectral Theory in Mathematical Physics