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Stationary diffusion on nonnegatively curved graphs

Contributed by Matěj Kripner, Václav Rozhoň, Robert Šámal, Martin Šindelář, Adrián Zámečník

Lazy random walk on a bounded-degree graph of nonnegative Ollivier–Ricci curvature has diffusive second moment and Gaussian upper tails when started in stationarity. If the maximum degree is $D$ , then $\mathbb E d(X_0,X_n)^2\le4Dn$ , with optimal order of dependence on $D$ . The results also hold for stationary random rooted infinite graphs. The proof combines known heat-kernel total-variation decay with a reversible energy identity for the conditional mean displacement. Its exponential form controls variation between starting vertices; martingale concentration then controls the walk itself.

Primarily AI-generated textHuman understanding: some partsOllivier-Ricci curvaturerandom walksreversibilitystationary displacement

Nov 04, 2026PDF ↗View work →

hexagon:2611.00051v1

math.IT — Information Theory

Least-Atom Extremizers for Resampling Noise

Contributed by Matěj Kripner, Václav Rozhoň, Robert Šámal, Martin Šindelář, Adrián Zámečník

A single least-mass atom determines the extremal behavior of resampling noise on a finite probability space. A fixed-moment comparison gives the sharp generalized Samorodnitsky inequality for every $1<q<2$ through one scalar curve, and identifies all nonconstant scalar extremizers. The same principle determines every $L^p$ -to- $L^q$ resampling norm for $1<p<q<\infty$ , resolving a conjecture of Cao, Fan, Han, Qiu, and Wang. The sharp hypercontractive parameter increases strictly with the least atom. The uniform-binary phase diagram is explicit, and product equality cases are classified for every nonuniform reference law and for the uniform binary law.

Primarily AI-generated textHuman understanding: some partsRenyi divergenceSamorodnitsky inequalitieshypercontractivityleast-atom extremizersresampling noise

Nov 04, 2026PDF ↗View work →

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Stationary diffusion on nonnegatively curved graphs

Least-Atom Extremizers for Resampling Noise

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