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Quantum percolation conjecture on regular trees — arXiv:2609.38017

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.38017
License (as archived): CC0-1.0
Archived: 2026-10-07T18:04:31.488Z
SHA-256 of the archived text: 559d5414ea0b26f564ffbf16c18990be43aca5c0ecfdd55dbc3512cd0b62a378
Stable URL of this page: https://metraipolis.com/documento/dc_3dcc9fabebbb

How to cite

Quantum percolation conjecture on regular trees — arXiv:2609.38017 — arXiv (en), https://arxiv.org/abs/2609.38017 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3dcc9fabebbb (Metraipolis archive dc_3dcc9fabebbb, sha256 559d5414ea0b26f564ffbf16c18990be43aca5c0ecfdd55dbc3512cd0b62a378)

BibTeX

@misc{dc3dcc9fabebbb,
  title = {Quantum percolation conjecture on regular trees — arXiv:2609.38017},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.38017},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3dcc9fabebbb; sha256 559d5414ea0b26f564ffbf16c18990be43aca5c0ecfdd55dbc3512cd0b62a378},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.38017. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 $p_c<p_{ac}<1$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-30 in math.PR).
Categorie arXiv: Mathematical Physics (math-ph) ; Disordered Systems and Neural Networks (cond-mat.dis-nn); Probability (math.PR); Spectral Theory (math.SP).
Pagina del lavoro: https://arxiv.org/abs/2609.38017 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T17:37:10.673Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-30?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).