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- W4301507967 abstract "The distances between flats of a Poisson $k$-flat process in the $d$-dimensional Euclidean space with $k<d/2$ are discussed. Continuing an approach originally due to Rolf Schneider, the number of pairs of flats having distance less than a given threshold and midpoint in a fixed compact and convex set is considered. For a family of increasing convex subsets, the asymptotic variance is computed and a central limit theorem with an explicit rate of convergence is proven. Moreover, the asymptotic distribution of the $m$-th smallest distance between two flats is investigated and it is shown that the ordered distances form asymptotically after suitable rescaling an inhomogeneous Poisson point process on the positive real axis. A similar result with a homogeneous limiting process is derived for distances around a fixed, strictly positive value. Our proofs rely on recent findings based on the Wiener-It^o chaos decomposition and the Malliavin-Stein method." @default.
- W4301507967 created "2022-10-05" @default.
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- W4301507967 date "2012-06-21" @default.
- W4301507967 modified "2023-10-16" @default.
- W4301507967 title "Distances between Poisson k-flats" @default.
- W4301507967 doi "https://doi.org/10.48550/arxiv.1206.4807" @default.
- W4301507967 hasPublicationYear "2012" @default.
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