Sharp Davies–Gaffney–Grigor’yan Lemma on graphs

Bauer, Frank; Hua, Bobo; Yau, Shing–Tung

doi:10.1007/s00208-017-1529-z

Cited by 19 publications

(12 citation statements)

References 20 publications

(19 reference statements)

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“…The following functional formulation of DGG Lemma on graphs is the key for proving our main theorems in this paper, see Theorem 1.1 in [3]. m with supp f ⊂ A, supp g ⊂ B, then (1) CD(n, K) for some K ∈ R.…”

Section: Notation and Main Resultsmentioning

confidence: 99%

Buser's inequality on infinite graphs

Liu

2019

Journal of Mathematical Analysis and Applications

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In this paper, we establish Buser type inequalities, i.e., upper bounds for eigenvalues in terms of Cheeger constants. We prove the Buser's inequality for an infinite but locally finite connected graph with Ricci curvature lower bounds. Furthermore, we derive that the graph with positive curvature is finite, especially for unbounded Laplacians. By proving Poincaré inequality, we obtain a lower bound on Cheeger constant in terms of positive curvature.

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Section: Notation and Main Resultsmentioning

confidence: 99%

Buser's inequality on infinite graphs

Liu

2019

Journal of Mathematical Analysis and Applications

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“…One of the most important features of the heat kernel is that its decay reflects the geometry of G, as is intuitively clear from the heat equation, and as is made precise by the theory of [1], as follows: First, suppose we are given a metric on G, that is a map ρ :…”

Section: Heat Kernelmentioning

confidence: 99%

Multi-Scale Analysis on Complex Networks using Hermitian Graph Wavelets

Gelbaum,

Titus,

Watson

2019

Preprint

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We construct and study a class of spectral graph wavelets by analogy with Hermitian wavelets on the real line. We provide a localization result that significantly improves upon those previously available, enabling application to highly non-sparse, even complete, weighted graphs. We then define a new measure of importance of a node within a network called the Maximum Diffusion Time, and conclude by establishing an equivalence between the maximum diffusion time and information centrality, thus suggesting applications to quantifying hierarchical and distributed leadership structures in groups of interacting agents.

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“…There is a trend in graph theory of studying discrete versions of concepts that classically appear in differential geometry (see for example [1], [2], [3], [5], [6], [7], [10], [9], [11], [13] , [16], [20], [22], [23], [24], [25]). In particular, a definition of Ricci curvature for graphs was given in 1999 by Schmuckenschläger.…”

Section: Introductionmentioning

confidence: 99%

Ricci curvature, graphs and eigenvalues

Siconolfi

2021

Preprint

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We express the discrete Ricci curvature of a graph as the minimal eigenvalue of a family of matrices, one for each vertex of a graph whose entries depend on the local adjaciency structure of the graph. Using this method we compute or bound the Ricci curvature of Cayley graphs of finite Coxeter groups and affine Weyl groups. As an application we obtain an isoperimetric inequality that holds for all Cayley graphs of finite Coxeter groups.

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Sharp Davies–Gaffney–Grigor’yan Lemma on graphs

Abstract: Abstract. In this note, we prove the sharp Davies-Gaffney-Grigor'yan lemma for minimal heat kernels on graphs.

Cited by 19 publications

References 20 publications

Buser's inequality on infinite graphs

Buser's inequality on infinite graphs

Multi-Scale Analysis on Complex Networks using Hermitian Graph Wavelets

Ricci curvature, graphs and eigenvalues

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