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arxiv: 1611.01059 · v1 · submitted 2016-11-03 · 🧮 math.SP · math.DS

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Diffusion on Delone sets

Sebastian Haeseler , Xueping Huang , Daniel Lenz , Felix Pogorzelski
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classification 🧮 math.SP math.DS
keywords graphsassociateddelonesetsapplyariseboundsconsider
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We consider graphs associated to Delone sets in Euclidean space. Such graphs arise in various ways from tilings. Here, we provide a unified framework. In this context, we study the associated Laplace operators and show Gaussian heat kernel bounds for their semigroups. These results apply to both metric and discrete graphs.

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