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}
}