Diffractive point sets with entropy
Abstract
After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of lattice gases. We show that taking the site occupation of a model set stochastically results, with probabilistic certainty, in well-defined diffractive properties augmented by a constant diffuse background. We discuss both the case of independent, but identically distributed (i.i.d.) random variables and that of independent, but different (i.e., site dependent) random variables. Several examples are shown.
Cite
@article{arxiv.math-ph/9809002,
title = {Diffractive point sets with entropy},
author = {M. Baake and R. V. Moody},
journal= {arXiv preprint arXiv:math-ph/9809002},
year = {2014}
}
Comments
25 pages; dedicated to Hans-Ude Nissen on the occasion of his 65th birthday; final version, some minor additions