Spectral Gaps for Jacobi Matrices on Graphs

2024/02/11 by Jonathan Breuer, Breuer, Jonathan, Eyal Seelig +1
Mathematics · #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2402.07202

openalex publication_date 2024/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• A Useful Formula for Periodic Jacobi Matrices on Trees
• Periodic Boundary Conditions for Periodic Jacobi Matrices on Trees
• Green matrix estimates of block Jacobi matrices II: Bounded gap in the essential spectrum
• A note on sharp spectral estimates for periodic Jacobi matrices
• On the Number of Closed Gaps of Discrete Periodic One-Dimensional Operators