Almost Sure Recovery in Quasi-periodic Structures

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 (Int Math Res Notices 1–19, 2020).

• Publication year

  2021

• Venue

  Journal of statistical physics

• Publication date

  2021-12-22

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1007/s10955-022-03059-2arXiv 2112.11613
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Recovering the Lattice From Its Random Perturbations

  2020influential reference
• Classification and statistics of cut-and-project sets

  2020cited by this paper
• Are quasicrystals really so rare in the Universe?

  2020cited by this paper
• Cloaking the underlying long-range order of randomly perturbed lattices.

  2020cited by this paper
• Hyperuniformity of quasicrystals

  2016cited by this paper
• Aperiodic crystals

  2016cited by this paper
• Natural quasicrystal with decagonal symmetry

  2015cited by this paper
• Equivalence relations on separated nets arising from linear toral flows

  2012cited by this paper
• Aperiodic Crystals: From Modulated Phases to Quasicrystals

  2007cited by this paper
• Basic properties of strong mixing conditions. A survey and some open questions

  2005cited by this paper
• Almost Periodic Measures and Long-Range Order in Meyer Sets

  2005cited by this paper
• Point Sets and Dynamical Systems In the Autocorrelation Topology

  2004cited by this paper
• SCD patterns have singular diffraction

  2004cited by this paper
• Point processes and stochastic displacement fields.

  2004cited by this paper
• Local density fluctuations, hyperuniformity, and order metrics.

  2003cited by this paper
• Quasicrystals and Almost Periodicity

  2002cited by this paper
• What is Aperiodic Order

  2002cited by this paper
• Diffraction from visible lattice points and kth power free integers

  1999cited by this paper
• Repetitive Delone sets and quasicrystals

  1999cited by this paper
• Meyer's concept of quasicrystal and quasiregular sets

  1996cited by this paper
• On diffraction by aperiodic structures

  1995cited by this paper
• Diffraction by aperiodic structures at high temperatures

  1995cited by this paper
• Basic Properties of Strong Mixing Conditions

  1985cited by this paper
• Metallic Phase with Long-Range Orientational Order and No Translational Symmetry

  1984cited by this paper
• An elementary proof of the strong law of large numbers

  1981cited by this paper
• Ecole d'été de probabilités de Saint-Flour VI-1976

  1977cited by this paper

• Stability of mathematical quasicrystals under statistical convergence

  2025influential citation
• Effective recovery of Fourier spectra and spectral approximation by finite groups

  2023cites this paper