2021/06/16 by Joachim Kerner, Pavlo Yatsyna, Kerner, Joachim +1
Mathematics · #05C38 #15A18 #34L15 #49R50 #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2106.08910
openalex publication_date 2021/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the spectral gap of the path graph and illustrate an interesting effect which has been described recently in the continuous setting. More explicitly, in the large-volume limit and in the presence of a certain external potential, it is shown that the spectral gap converges to zero strictly faster than it does for the free Laplacian. The underlying mechanism is a combination of the increase in volume and an effective degeneracy of the ground state in the limiting regime.