Random Spherical Disc-Polygons in a Spherical Spindle Convex Disc
In this paper, we consider the asymptotic behaviour of the expectation of the number of vertices of a uniform random spherical disc-polygon. This provides a connection between the corresponding results in spherical convexity, and in Euclidean spindle-convexity, where the expectation tends to the sam...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2024
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| Sorozat: | STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
61 No. 3 |
| Tárgyszavak: | |
| doi: | 10.1556/012.2024.04315 |
| mtmt: | 35444867 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/38596 |
| Tartalmi kivonat: | In this paper, we consider the asymptotic behaviour of the expectation of the number of vertices of a uniform random spherical disc-polygon. This provides a connection between the corresponding results in spherical convexity, and in Euclidean spindle-convexity, where the expectation tends to the same constant. We also extend the result to a more general case, where the random points generating the uniform random disc-polygon are chosen from spherical convex disc with smooth boundary. |
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| Terjedelem/Fizikai jellemzők: | 215-230 |
| ISSN: | 0081-6906 |