2025/08/22 by Matthias Hofmann, Joachim Kerner, Hofmann, Matthias +3
Mathematics · #Class (philosophy) #Conjecture #Graph #Graph theory and applications #Limit (mathematics) #Numerical methods in inverse problems #Path (computing) #Spectral Theory in Mathematical Physics #Spectral gap #Spectral properties #Spectrum (functional analysis) #Zero (linguistics)
paper · pdf · doi:10.1177/09217134261465640
openalex created_date 2025/10/10 · openalex publication_date 2026/07/15 · openalex updated_date 2026/08/01
In this note, we elaborate on the asymptotic behavior of the spectral gap of a class of discrete Schrödinger operators defined on a path graph in the limit of infinite volume. We confirm recent results and generalize them to a larger class of potentials using entirely different methods. Notably, we also resolve a conjecture previously proposed in this context. This then yields new insights into the rate at which the spectral gap tends to zero as the volume increases.