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Neighbour-count dependent thinning of Poisson processes: correlation structure and Poisson approximation
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
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