Abstract:We prove that every transitive graph of non-negative Ollivier-Ricci curvature has polynomial growth. We deduce from this and a theorem of Brena and Brue that a finitely generated group admits a Cayley graph of non-negative Ollivier-Ricci curvature if and only if it is virtually abelian. Beyond the transitive setting, we also prove a quasi-polynomial $r^{O(\sqrt{\log r})}$ volume bound for balls around typical vertices in finite bounded-degree graphs of non-negative Ollivier-Ricci curvature, greatly strengthening a theorem of Salez (GAFA 2022).
From: Tom Hutchcroft [view email]
[v1]
Wed, 3 Dec 2025 16:58:46 UTC (41 KB)
[v2]
Fri, 28 Aug 2026 15:34:02 UTC (45 KB)
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