Pointwise subexponential growth and near-diffusive displacement on bounded-degree graphs with non-negative Ollivier--Ricci curvature

Chiyu Zhou

probability theory

Pointwise subexponential growth and near-diffusive displacement on bounded-degree graphs with non-negative Ollivier--Ricci curvature

arXiv:2607.27162

summary

The paper establishes subexponential upper bounds on the displacement of continuous-time random walks and on volume growth for locally finite graphs with bounded degree and non‑negative Ollivier–Ricci curvature.

Abstract

Let $G = (V, E)$ be a possibly infinite, locally finite graph with non-negative Ollivier--Ricci curvature and degrees bounded by $d < \infty$ . We prove that there exists a constant $C_{d}$ such that the continuous-time random walk displacement and log-volume growth satisfy \[ \mathbb{E}_x \mathrm{dist}(x,X_t)^2 \le t \exp\left[C_d \sqrt{\log t \log\log t}\right], \] \[ \log \mathrm{Vol}(B(x,r)) \le \exp\left[C_d \sqrt{\log r \log\log r}\right], \] for every $x \in V$ and all $r, t \geq e^{e}$ .

23 pages

Topics & keywords

#random walks #ollivier-ricci curvature #graph growth #subexponential bounds #bounded-degree graphsOllivier–Ricci curvaturecontinuous-time random walkvolume growthdisplacement boundsubexponential growth