The regular tree Anderson model at low disorder

2025/11/13 by Reuben Drogin, Charles K. Smart, Drogin, Reuben +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum many-body systems #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2511.10564

openalex publication_date 2025/11/13 · openalex created_date 2025/11/15 · openalex updated_date 2026/07/28

Abstract

We prove delocalization for the Anderson model on an infinite regular tree (or Cayley graph or Bethe lattice) at low disorder. This extends earlier results of Klein and Aizenman--Warzel by filling in the previously missing parts of the spectrum. Our argument generalizes to any disorder with small fourth moment and sufficiently regular density. We prove continuity of the Lyapunov exponent as the disorder vanishes.

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