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- W2894462688 abstract "We study a stable partial matching $tau$ of the (possibly randomized) $d$-dimensional lattice with a stationary determinantal point process $Psi$ on $mathbb{R}^d$ with intensity $alpha>1$. For instance, $Psi$ might be a Poisson process. The matched points from $Psi$ form a stationary and ergodic (under lattice shifts) point process $Psi^tau$ with intensity $1$ that very much resembles $Psi$ for $alpha$ close to $1$. On the other hand $Psi^tau$ is hyperuniform and number rigid, quite in contrast to a Poisson process. We deduce these properties by proving more general results for a stationary point process $Psi$, whose so-called matching flower (a stopping set determining the matching partner of a lattice point) has a certain subexponential tail behaviour. For hyperuniformity, we also additionally need to assume some mixing condition on $Psi$. Further, if $Psi$ is a Poisson process then $Psi^tau$ has an exponentially decreasing truncated pair correlation function." @default.
- W2894462688 created "2018-10-05" @default.
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- W2894462688 date "2018-09-29" @default.
- W2894462688 modified "2023-10-18" @default.
- W2894462688 title "Hyperuniform and rigid stable matchings" @default.
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- W2894462688 doi "https://doi.org/10.48550/arxiv.1810.00265" @default.
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