Diffusion on Delone sets
Sebastian Haeseler, Xueping Huang, Daniel Lenz, Felix Pogorzelski
TL;DR
This paper studies graphs derived from Delone sets in Euclidean space, providing a unified framework to analyze their Laplace operators and establishing Gaussian heat kernel bounds for their semigroups, applicable to both metric and discrete graphs.
Contribution
It introduces a unified framework for graphs from Delone sets and proves Gaussian heat kernel bounds for their Laplace operators.
Findings
Gaussian heat kernel bounds established
Applicable to both metric and discrete graphs
Unified framework for graphs from Delone sets
Abstract
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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