Diffraction of the dart–rhombus random tiling

Letters in Mathematical Physics

Sing

2004

Section: Theorem 1 Suppose That For a Lattice Gas Model On Z D Withmentioning

confidence: 99%

Diffraction Spectrum of Lattice Gas Models above T_c

Letters in Mathematical Physics

Sing

2004

“…Let Γ be a lattice in an LCA group G whose topology has a countable base, and let ω = t∈Γ w(t)δ t be a Dirac comb on Γ with bounded complex weights. Let an averaging sequence U = {U i | i ∈ N} be given which constitutes a monotone increasing van Hove sequence, and assume that the corresponding autocorrelation measure γ ω of (12) exists. Then we have:…”

Section: Theoremmentioning

confidence: 99%

Diffraction of Weighted Lattice Subsets

2002

Can. math. bull.

Abstract. A Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice Γ inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a continuous function and the uniform lattice Dirac comb, and its diffraction measure is periodic, with the dual lattice Γ * as lattice of periods. This statement remains true in the setting of a locally compact Abelian group whose topology has a countable base.

“…Let us remark that an analogous scenario, with the same type of result, occurs for the more complicated dart-rhombus random tiling, see [25] for details.…”

Section: Domino Tilingmentioning

confidence: 57%

“…= p n = 1/n, S 0 = M and S 1 = 0. In this limit, (25) gives back the corresponding result of Proposition 1. Also, one can treat more general cases of Markov chains, compare [17, vol.…”

Section: Bernoulli and Markov Systemsmentioning

confidence: 60%

Untitled

Journal of Statistical Physics

Höffe

2000

Self Cite

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.