Neighbour-count dependent thinning of Poisson processes: correlation structure and Poisson approximation
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914156113821696 |
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| author | Hlyniana, Kateryna |
| author_facet | Hlyniana, Kateryna |
| contents | We study a local thinning $T_r$ that retains a point with probability $p(n_r)$, where $n_r$ counts neighbors within radius $r$. For Poisson input with spatially varying intensity, we obtain an exact intensity via a Poisson--mixture formula and a small-radius expansion. For homogeneous input we give a closed-form pair correlation based on the three-region overlap . First-order contact-scale asymptotics identify how the values $p(0),p(1),p(2)$ govern inhibition or clustering. On bounded windows we approximate $T_r(X)$ by a Poisson process with matched intensity through three routes: (i) a direct coupling to an independent thinning giving a total-variation bound; (ii) a Laplace-functional error supported at distances $\le 2r$ and of order $|W|\,λ^2 r^d$; and (iii) a Stein bound in the Barbour--Brown $d_2$ metric controlled by $\int_{\|h\|\le 2r} |g(h)-1|\,dh$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neighbour-count dependent thinning of Poisson processes: correlation structure and Poisson approximation Hlyniana, Kateryna Probability We study a local thinning $T_r$ that retains a point with probability $p(n_r)$, where $n_r$ counts neighbors within radius $r$. For Poisson input with spatially varying intensity, we obtain an exact intensity via a Poisson--mixture formula and a small-radius expansion. For homogeneous input we give a closed-form pair correlation based on the three-region overlap . First-order contact-scale asymptotics identify how the values $p(0),p(1),p(2)$ govern inhibition or clustering. On bounded windows we approximate $T_r(X)$ by a Poisson process with matched intensity through three routes: (i) a direct coupling to an independent thinning giving a total-variation bound; (ii) a Laplace-functional error supported at distances $\le 2r$ and of order $|W|\,λ^2 r^d$; and (iii) a Stein bound in the Barbour--Brown $d_2$ metric controlled by $\int_{\|h\|\le 2r} |g(h)-1|\,dh$. |
| title | Neighbour-count dependent thinning of Poisson processes: correlation structure and Poisson approximation |
| topic | Probability |
| url | https://arxiv.org/abs/2511.10083 |