Diffusion on Delone sets
  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. 
Sebastian Haeseler, Xueping Huang, Daniel Lenz, Felix Pogorzelski
math.SP math.DS