English

Optimal matchings of randomly perturbed lattices

Probability 2025-06-23 v1

Abstract

Consider a point process in Euclidean space obtained by perturbing the integer lattice with independent and identically distributed random vectors. Under mild assumptions on the law of the perturbations, we construct a translation-invariant perfect matching between this point process and the lattice, such that the matching distance has the same tail behavior as the hole probability of the point process, which is a natural lower bound.

Keywords

Cite

@article{arxiv.2506.16873,
  title  = {Optimal matchings of randomly perturbed lattices},
  author = {Dor Elboim and Yinon Spinka and Oren Yakir},
  journal= {arXiv preprint arXiv:2506.16873},
  year   = {2025}
}