论文标题
较低的RICCI曲率结合的有向图上的热流量和度量浓度
Heat flow and concentration of measure on directed graphs with a lower Ricci curvature bound
论文作者
论文摘要
在先前的作品中，作者引入了lin-lu-yau类型的RICCI曲率，用于指向钟拉普拉斯（Chung Laplacian）的有向图。本说明的目的是通过热量半流群的梯度估计和沿热流的运输不平等，提供我们下部RICCI曲率的表征。作为一种应用，我们将结论一下阳性RICCI曲率的有向图的量度不平等。
In a previous work, the authors introduced a Lin-Lu-Yau type Ricci curvature for directed graphs referring to the formulation of the Chung Laplacian. The aim of this note is to provide a von Renesse-Sturm type characterization of our lower Ricci curvature bound via a gradient estimate for the heat semigroup, and a transportation inequality along the heat flow. As an application, we will conclude a concentration of measure inequality for directed graphs of positive Ricci curvature.
