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Linear Cotype Bounds for Nonlinear Spectral Gaps of Scalar Expanders — arXiv:2611.05649

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.05649
License (as archived): CC0-1.0
Archived: 2026-11-05T18:28:39.434Z
SHA-256 of the archived text: 870c3e6c00c7f7a4641af98bf2284cd8c9d5afcb055c4c05c478496b4037427e
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How to cite

Linear Cotype Bounds for Nonlinear Spectral Gaps of Scalar Expanders — arXiv:2611.05649 — arXiv (en), https://arxiv.org/abs/2611.05649 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cfffe1fa1cd7 (Metraipolis archive dc_cfffe1fa1cd7, sha256 870c3e6c00c7f7a4641af98bf2284cd8c9d5afcb055c4c05c478496b4037427e)

BibTeX

@misc{dccfffe1fa1cd7,
  title = {Linear Cotype Bounds for Nonlinear Spectral Gaps of Scalar Expanders — arXiv:2611.05649},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.05649},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cfffe1fa1cd7; sha256 870c3e6c00c7f7a4641af98bf2284cd8c9d5afcb055c4c05c478496b4037427e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.05649. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let $G$ be a finite simple $d$-regular graph, $d\geq 3$, whose second largest adjacency eigenvalue satisfies $\lambda_2(G)\leq (1-\delta)d$, where $0<\delta\leq 1$. We prove that the Poincaré constant satisfies $$\gamma(G,\|\cdot\|_X)\lesssim \frac{qCK}{\delta}$$ whenever $X$ is a real Banach space with a $K$-unconditional Schauder basis and cotype $q$ with constant $C$. This constant compares the mean distance over all vertex pairs with the mean distance across edges. For real Banach lattices the bound is $O(qC/\delta)$. The proof estimates where a random walk first leaves each coordinate level set. As a consequence of the bound, if $n$-vertex graphs in a fixed-degree expander family embed with bounded distortion into spaces with bounded $C,K$, then $q$ must grow at least as fast as $\log n$. This order is attained in $\ell_q^n$.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Functional Analysis (math.FA) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2611.05649 — 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 2026-11-05T18:18:34.004Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).