论文标题
帽子型直径的注释，该直径绑定为呈熵RICCI曲率的图形
A note on a Bonnet-Myers type diameter bound for graphs with positive entropic Ricci curvature
论文作者
论文摘要
根据全球梯度估计给出了离散空间上的熵RICCI曲率的等效定义。通过特殊选择密度函数$ρ$，我们获得了局部梯度估计，该梯度又使我们能够为具有正熵RICCI曲率的图形绑定的引擎盖式式型直径。但是，高管的情况表明界限可能不是最佳的（默认情况下，选择$θ$是对数均值）。如果$θ$是算术平均值，则可以恢复Bakry-émery标准，并且直径结合是最佳的，因为HyperCubes可以实现它。
An equivalent definition of entropic Ricci curvature on discrete spaces was given in terms of the global gradient estimate. With a particular choice of the density function $ρ$, we obtain a localized gradient estimate, which in turns allow us to derive a Bonnet-Myers type diameter bound for graphs with positive entropic Ricci curvature. However, the case of the hypercubes indicates that the bound may be not optimal (where $θ$ is chosen to be logarithmic mean by default). If $θ$ is arithmetic mean, the Bakry-Émery criterion can be recovered and the diameter bound is optimal as it can be attained by the hypercubes.
