Ricci curvature and eigenvalue estimate on locally finite graphs

By Yong Lin, Shing-Tung Yau. 2010

272 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/07cb3055dbc6392f2bdc523f23d1f0c911a06890

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Li-Yau inequality on graphs (2013, background): “[8, 16, 17, 20, 21, 23]).”
Li–Yau inequality on finite graphs via non-linear curvature dimension conditions (2014, background): “On graphs, it has been studied in [5, 6, 10, 13, 15, 16].”
Bakry–Émery Curvature Functions on Graphs (2016, background): “● All abelian Cayley graphs lie in the class CD(0,∞) [7, 16, 19].”
Bakry–Émery curvature and diameter bounds on graphs (2016, methodology): “In this article, we focus on Bakry-Émery-Ricci-curvature [1, 21, 16, 13].”
Displacement convexity of entropy and related inequalities on graphs (2012, background): “However, while a lot is nowknown in the Riemannian setting (and more generally in geodesic spaces), very little is known so far in discrete spaces (such as finite graphs or finite Markov chains), with the notable exception of some notions of (discrete) Ricci curvature proposed recently by several au”
Curvature and transport inequalities for Markov chains in discrete spaces (2015, background): “In the discrete setting, this curvature condition was first studied in [41] and then in [5,6,10, 29].”
Volume growth, spectrum and stochastic completeness of infinite graphs (2011, background): “See also the recent work on Ricci curvature of graphs [3,35,42].”
Ricci Curvature of Finite Markov Chains via Convexity of the Entropy (2011, methodology): “Another approach has been taken by Lin and Yau [26], who defined Ricci curvature in terms the heat semigroup.”
On quotients of spaces with Ricci curvature bounded below (2017, methodology): “Following Bakry-Émery [10, 51] we define the Γ2-functional (carrÈ-du-champ itÈrÈ ) as follows: 2Γ2(f, g) = ∆(Γ(f, g))− Γ(f,∆g)− Γ(∆f, g).”
Gradient flows of the entropy for finite Markov chains (2011, unknown): “Yau [16] studied Ricci curvature on graphs by taking a characterisation in terms of the heat semigroup due to Bakry and Emery as a definition.”
On the spectrum of hypergraphs (2017, methodology): “2 in [23], we can express our Ricci curvature operator on a hypergraph G as Γ2(f, f)(i) = 1 4 1 di ∑”
Ricci curvature of graphs (2011, background): “For a more general definition of Ricci curvature, in [17], Lin and Yau give a generalization of lower Ricci curvature bound in the framework of graphs.”