Note on the variance of generalized random polygons
We consider a probability model in which the hull of a sample of i.i.d. uniform random points from a convex disc K is formed by the intersection of all translates of another suitable fixed convex disc L that contain the sample. Such an object is called a random L -polygon in K . We assume that both...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2025
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| Sorozat: | AEQUATIONES MATHEMATICAE
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| Tárgyszavak: | |
| doi: | 10.1007/s00010-024-01147-0 |
| mtmt: | 35681499 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/35542 |
| Tartalmi kivonat: | We consider a probability model in which the hull of a sample of i.i.d. uniform random points from a convex disc K is formed by the intersection of all translates of another suitable fixed convex disc L that contain the sample. Such an object is called a random L -polygon in K . We assume that both K and L have C^2_+ C + 2 smooth boundaries, and we prove upper bounds on the variance of the number of vertices and missed area of random L -polygons assuming different curvature conditions. We also transfer some of our result to a circumscribed variant of this model. |
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| ISSN: | 0001-9054 |