Almost sure recovery in quasi-periodic structures
arXiv:2112.11613 · doi:10.1007/s10955-022-03059-2
Abstract
We study random perturbations of quasi-periodic uniformly discrete sets in the -dimensional euclidean space. By means of Diffraction Theory, we find conditions under which a quasi-periodic set can be almost surely recovered from its random perturbations. This extends the recent periodic case result of Yakir from "Recovery the lattice from its random perturbations" IMRN 2020 (arXiv:200201508).
24 pages. Key words: quasi-crystals, mathematical diffraction, stationarity. Comments to V3: Final version. To appear in Journal of Statistical Physics