Year: 2026
Type: preprint
Abstract: For Bernoulli bond percolation on every regular tree of degree at least three, we prove that infinite clusters appear strictly before absolutely continuous spectrum. Throughout an explicit supercritical interval, the adjacency operator of every open cluster almost surely has no absolutely continuous component. Together with Bordenave's theorem, this gives $p_c
Source: arXiv (Cornell University)
Authors: Becker, Simon, Oltman, Izak
Institutions: Bocconi University, Northwestern University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214889298