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arXiv · 2601.08983

Optimal factor matchings for point processes on non-amenable unimodular graphs

Yinon Spinka·Oren Yakir
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Abstract

Consider a unit-intensity point process $\Pi$ on the vertex set $V$ of a transitive non-amenable unimodular graph. We study invariant matchings between $\Pi$ and $V$ having small typical matching distances. When $\Pi$ is either a Poisson process or i.i.d. perturbations of the vertex set, we determine the optimal matching distance and show that it can be attained by a factor matching scheme (that is, a deterministic and equivariant function of $\Pi$).

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Yinon Spinka, Oren Yakir. 2026-01-13. Optimal factor matchings for point processes on non-amenable unimodular graphs. https://arxiv.org/abs/2601.08983

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