Diffusion on Delone sets. (English) Zbl 1380.37034
Graphs associated to Delone sets or tilings appear in many ways in the study of Schrödinger operators for quasicrystals and (dis)ordered structures. Here, the authors look at operators of Laplace type from a diffusion point of view. A systematic framework via neighbour relations is presented. It covers both metric and discrete graphs. The authors then establish Gaussian heat kernel estimates for both classes, thus unifying and extending existing results in this setting.
Reviewer: Michael Baake (Bielefeld)
MSC:
| 37B50 | Multi-dimensional shifts of finite type, tiling dynamics (MSC2010) |
| 05B45 | Combinatorial aspects of tessellation and tiling problems |
| 52C23 | Quasicrystals and aperiodic tilings in discrete geometry |
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