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Diffusion on Delone sets

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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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Notes

  1. By adding points on the edges one can then automatically ensure that the edge lengths are bounded from above as well.

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Acknowledgements

The authors gratefully acknowledge financial support from DFG. D.L. would also like to thank Peter Stollmann and Ivan Veselić for delightful discussions on quantum graphs. X.H. was partially supported by The Startup Foundation for Introducing Talent of NUIST (Grant No. 2015r053) and NSFC (Grant No. 11601238). F.P. was supported in part by a Technion Fine fellowship.

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Authors and Affiliations

  1. Mathematisches Institut, Friedrich Schiller Universität Jena, 07743, Jena, Germany

    Sebastian Haeseler & Daniel Lenz

  2. Department of Mathematics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Xueping Huang

  3. Technion Israel Institute of Technology Haifa, 32000, Haifa, Israel

    Felix Pogorzelski

Authors
  1. Sebastian Haeseler
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  2. Xueping Huang
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  3. Daniel Lenz
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  4. Felix Pogorzelski
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Correspondence to Daniel Lenz.

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Haeseler, S., Huang, X., Lenz, D. et al. Diffusion on Delone sets. J Stat Phys 167, 1496–1510 (2017). https://doi.org/10.1007/s10955-017-1779-x

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  • DOI: https://doi.org/10.1007/s10955-017-1779-x

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