Hirsch, Christian and Jahnel, Benedikt and Tóbiás, András József (2020) Lower large deviations for geometric functionals. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 25. pp. 1-12. ISSN 1083-589X
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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.
| Item Type: | Article |
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| Additional Information: | Export Date: 18 August 2025; Cited By: 4 |
| Uncontrolled Keywords: | large deviations; lower tails; stabilizing functionals; random geometric graph; k-nearest neighbor graph; relative neighborhood graph; Voronoi tessellation; clique count. |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 04 Sep 2025 08:29 |
| Last Modified: | 04 Sep 2025 08:29 |
| URI: | https://real.mtak.hu/id/eprint/223394 |
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