English

The regular tree Anderson model at low disorder

Probability 2025-11-14 v1 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2511.10564,
  title  = {The regular tree Anderson model at low disorder},
  author = {Reuben Drogin and Charles K Smart},
  journal= {arXiv preprint arXiv:2511.10564},
  year   = {2025}
}
R2 v1 2026-07-01T07:36:15.616Z