The diffraction of various random subsets of the integer lattice
Zd, such as the coin tossing and related systems, are well
understood. Here, we go one important step beyond and consider random point
sets in Rd. We present several systems with an effective
stochastic interaction that still allow for explicit calculations of the
autocorrelation and the diffraction measure. We concentrate on one-dimensional
examples for illustrative purposes, and briefly indicate possible
generalisations to higher dimensions.
In particular, we discuss the stationary Poisson process in Rd
and the renewal process on the line. The latter permits a unified approach to a
rather large class of one-dimensional structures, including random tilings.
Moreover, we present some stationary point processes that are derived from the
classical random matrix ensembles as introduced in the pioneering work of Dyson
and Ginibre. Their re-consideration from the diffraction point of view improves
the intuition on systems with randomness and mixed spectra.Comment: 9 pages, 2 figures; talk presented at ICQ 11 (Sapporo