Fitting regular point patterns with a hyperuniform perturbed lattice

We introduce a new methodology for modeling regular spatial data using hyperuniform point processes. We show that, under some mixing conditions on the perturbations, perturbed lattices in general dimension are hyperuniform. Due to their inherent repulsive structure, they serve as an effective baseline model for data sets in which points exhibit repulsiveness. Specifically, we derive an explicit formula for the $K$-function of lattices perturbed by a Gaussian random field, which proves particularly useful in conjunction with the minimal contrast method. We apply this approach to a data set representing the grain centers of a polycrystalline metallic material composed of nickel and titanium.

• Publication year

  2025

• Venue

  Unknown venue

• Publication date

  2025-03-15

• Fields of study

  Materials Science, Physics, Mathematics

• Identifiers
  arXiv 2503.12179
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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