Journal of Statistical Physics

, Volume 99, Issue 1–2, pp 219–261 | Cite as

Diffraction of Random Tilings: Some Rigorous Results

  • Michael Baake
  • Moritz Höffe
Article

Abstract

The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of stochastic product tilings built from cuboids, and of planar random tilings based on solvable dimer models, augmented by a brief outline of the diffraction from the classical 2D Ising lattice gas. We also give a summary of the measure theoretic approach to mathematical diffraction theory which underlies the unique decomposition of the diffraction spectrum into its pure point, singular continuous, and absolutely continuous parts.

diffraction theory stochastic point sets random tilings quasicrystals 

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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Michael Baake
    • 1
  • Moritz Höffe
    • 1
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenGermany

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