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arXiv · 2011.11418

Heat flow and concentration of measure on directed graphs with a lower Ricci curvature bound

Ryunosuke Ozawa·Yohei Sakurai·Taiki Yamada
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Abstract

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.

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Ryunosuke Ozawa, Yohei Sakurai, Taiki Yamada. 2020-11-20. Heat flow and concentration of measure on directed graphs with a lower Ricci curvature bound. https://arxiv.org/abs/2011.11418

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