Optimal factor matchings for point processes on non-amenable unimodular graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912822812737536 |
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| author | Spinka, Yinon Yakir, Oren |
| author_facet | Spinka, Yinon Yakir, Oren |
| contents | Consider a unit-intensity point process $Π$ on the vertex set $V$ of a transitive non-amenable unimodular graph. We study invariant matchings between $Π$ and $V$ having small typical matching distances. When $Π$ 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 $Π$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08983 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal factor matchings for point processes on non-amenable unimodular graphs Spinka, Yinon Yakir, Oren Probability Combinatorics Consider a unit-intensity point process $Π$ on the vertex set $V$ of a transitive non-amenable unimodular graph. We study invariant matchings between $Π$ and $V$ having small typical matching distances. When $Π$ 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 $Π$). |
| title | Optimal factor matchings for point processes on non-amenable unimodular graphs |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2601.08983 |