Výsledky vyhledávání - "OZAWA, RYUNOSUKE"

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

Autor: Ozawa, Ryunosuke, Sakurai, Yohei, Yamada, Taiki

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 curv

Externí odkaz: http://arxiv.org/abs/2011.11418

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Maximal diameter theorem for directed graphs of positive Ricci curvature

Autor: Ozawa, Ryunosuke, Sakurai, Yohei, Yamada, Taiki

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 investigate rigidity properties for the equality case, and conclude a ma

Externí odkaz: http://arxiv.org/abs/2011.00755

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Geometric and spectral properties of directed graphs under a lower Ricci curvature bound

Autor: Ozawa, Ryunosuke, Sakurai, Yohei, Yamada, Taiki

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 discuss generalization problem of their Ricci curvature for directed graphs

Externí odkaz: http://arxiv.org/abs/1909.07715

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Estimate of observable diameter of $l_p$-product spaces

Autor: Ozawa, Ryunosuke, Shioya, Takashi

We estimate the observable diameter of the $l_p$-product space $X^n$ of an mm-space $X$ by using the limit formula in our previous paper. The idea of our proof is based on Gromov's book. As a corollary we obtain the phase transition property of $\{X^

Externí odkaz: http://arxiv.org/abs/1404.2679

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Limit formulas for metric measure invariants and phase transition property

Autor: Ozawa, Ryunosuke, Shioya, Takashi

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 convergent sequence of pyramids. We obtain various applications of our limit f

Externí odkaz: http://arxiv.org/abs/1402.6831

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