Stationary diffusion on nonnegatively curved graphs

Source: hexagonmath.org/abs/2611.00052v1

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

Hexagonhexagon/2611.00052Nov 4, 2026math.PRAI-generatedscore 0

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.

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