2 citations · 4 across the 5 of their papers we have counts for
5 papers
Heat flow and concentration of measure on directed graphs with a lower Ricci curvature bound
Ryunosuke Ozawa, Yohei Sakurai, Taiki Yamada
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 pro…
Maximal diameter theorem for directed graphs of positive Ricci curvature
Ryunosuke Ozawa, Yohei Sakurai, Taiki Yamada
In a previous work, the authors have introduced a Lin-Lu-Yau type Ricci curvature for directed graphs, and obtained a diameter comparison of Bonnet-Myers type. In this paper, we in…
Geometric and spectral properties of directed graphs under a lower Ricci curvature bound
Ryunosuke Ozawa, Yohei Sakurai, Taiki Yamada
For undirected graphs, the Ricci curvature introduced by Lin-Lu-Yau has been widely studied from various perspectives, especially geometric analysis. In the present paper, we discu…
Estimate of observable diameter of -product spaces
Ryunosuke Ozawa, Takashi Shioya
We estimate the observable diameter of the -product space of an mm-space by using the limit formula in our previous paper. The idea of our proof is based on Gromov's…
Limit formulas for metric measure invariants and phase transition property
Ryunosuke Ozawa, Takashi Shioya
We generalize the observable diameter and the separation distance for metric measure spaces to those for pyramids, and prove some limit formulas for these invariants for a converge…