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2020 Lower large deviations for geometric functionals
Christian Hirsch, Benedikt Jahnel, András Tóbiás
Electron. Commun. Probab. 25(none): 1-12 (2020). DOI: 10.1214/20-ECP322

Abstract

This work develops a methodology for analyzing large-deviation lower tails associated with geometric functionals computed on a homogeneous Poisson point process. The technique applies to characteristics expressed in terms of stabilizing score functions exhibiting suitable monotonicity properties. We apply our results to clique counts in the random geometric graph, intrinsic volumes of Poisson–Voronoi cells, as well as power-weighted edge lengths in the random geometric, $k$-nearest neighbor and relative neighborhood graph.

Citation

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Christian Hirsch. Benedikt Jahnel. András Tóbiás. "Lower large deviations for geometric functionals." Electron. Commun. Probab. 25 1 - 12, 2020. https://doi.org/10.1214/20-ECP322

Information

Received: 15 October 2019; Accepted: 19 May 2020; Published: 2020
First available in Project Euclid: 16 June 2020

zbMATH: 07225534
MathSciNet: MR4112772
Digital Object Identifier: 10.1214/20-ECP322

Subjects:
Primary: 60F10, 60K35, 82C22

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