Optimal matchings of randomly perturbed lattices

Dor Elboim; Yinon Spinka; Oren Yakir

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arXiv · 2506.16873

Optimal matchings of randomly perturbed lattices

Dor Elboim·Yinon Spinka·Oren Yakir

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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.

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Dor Elboim, Yinon Spinka, Oren Yakir. 2025-06-20. Optimal matchings of randomly perturbed lattices. https://arxiv.org/abs/2506.16873

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