Almost sure recovery in quasi-periodic structures

TL;DR

This paper investigates conditions under which quasi-periodic structures can be almost surely recovered from their randomly perturbed versions using diffraction theory, extending previous results from periodic to quasi-periodic cases.

Contribution

It introduces new conditions for recovery of quasi-periodic sets from random perturbations, generalizing prior work on periodic structures.

Findings

Recovery conditions established for quasi-periodic sets

Extension of periodic case results to quasi-periodic structures

Application of diffraction theory to perturbation analysis

Abstract

We study random perturbations of quasi-periodic uniformly discrete sets in the $d$-dimensional euclidean space. By means of Diffraction Theory, we find conditions under which a quasi-periodic set $X$ 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).