Heat flow and concentration of measure on directed graphs with a lower Ricci curvature bound
Heat flow and concentration of measure on directed graphs with a lower Ricci curvature bound
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具有下里奇曲率界的有向图上的热流和测量浓度
DOI：
10.1007/s11118-022-09994-9
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发表时间：
2022
影响因子：
1.1
通讯作者：
T. Yamada,
中科院分区：
文献类型：
--
作者：
R. Ozawa;Y. Sakurai;T. Yamada,
在以前的工作（小泽等人计算。变种部分差异Equ.59（4），39），作者引入了有向图的Lin-Lu-Yau型Ricci曲率，并引用了Chung Laplacian的公式.本文的目的是通过热半群的梯度估计和热流沿着的输运不等式，给出我们的Ricci曲率下界的vonRenesse-Sturm型刻画.作为应用，我们将得到正Ricci曲率有向图的一个集中测度不等式。
In a previous work (Ozawa et al. Calc. Var. Partial Diff. Equ.59(4), 39 ), 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.