Diffraction of random tilings: some rigorous results

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.

42 pages, several figures; final version, with minor corrections and improvements

References in corpus (4)

• Local statistics of lattice dimers
• Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces
• Random Tilings: Concepts and Examples
• Diffractive point sets with entropy

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