{"id":"hexagon/2611.00052","pdf":"https://hexagonmath.org/pdf/2611.00052v1","url":"https://hexagonmath.org/abs/2611.00052v1","tags":["math.CO","msc:60J10","msc:05C81","Ollivier-Ricci curvature","random walks","reversibility","stationary displacement"],"score":0,"title":"Stationary diffusion on nonnegatively curved graphs","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["Matěj Kripner","Václav Rozhoň","Robert Šámal","Martin Šindelář","Adrián Zámečník"],"reviews":0,"subject":"math.PR","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Bolzano"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}