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- W4366458529 abstract "We prove a large deviation principle for the point process of large Poisson $k$-nearest neighbor balls in hyperbolic space. More precisely, we consider a stationary Poisson point process of unit intensity in a growing sampling window in hyperbolic space. We further take a growing sequence of thresholds such that there is a diverging expected number of Poisson points whose $k$-nearest neighbor ball has a volume exceeding this threshold. Then, the point process of exceedances satisfies a large deviation principle whose rate function is described in terms of a relative entropy. The proof relies on a fine coarse-graining technique such that inside the resulting blocks the exceedances are approximated by independent Poisson point processes." @default.
- W4366458529 created "2023-04-22" @default.
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- W4366458529 date "2023-04-18" @default.
- W4366458529 modified "2023-09-25" @default.
- W4366458529 title "Large deviations for hyperbolic $k$-nearest neighbor balls" @default.
- W4366458529 doi "https://doi.org/10.48550/arxiv.2304.08744" @default.
- W4366458529 hasPublicationYear "2023" @default.
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