Second-order properties for planar Mondrian tessellations
- In this paper planar STIT tessellations with weighted axis-parallel cutting directions are considered. They are known also as weighted planar Mondrian tessellations in the machine learning literature, where they are used in random forest learning and kernel methods. Various second-order properties of such random tessellations are derived, in particular, explicit formulas are obtained for suitably adapted versions of the pair- and cross-correlation functions of the length measure on the edge skeleton and the vertex point process. Also, explicit formulas and the asymptotic behaviour of variances are discussed in detail.
| Author: | Carina BetkenGND, Tom KaufmannGND, Kathrin MeierGND, Christoph ThäleGND |
|---|---|
| URN: | urn:nbn:de:hbz:294-125226 |
| DOI: | https://doi.org/10.1007/s11009-023-10017-2 |
| Parent Title (English): | Methodology and computing in applied probability |
| Publisher: | Springer Nature |
| Place of publication: | Berlin |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2024/04/08 |
| Date of first Publication: | 2023/03/24 |
| Publishing Institution: | Ruhr-Universität Bochum, Universitätsbibliothek |
| Tag: | Cross-correlation function; Mondrian tessellation; Pair-correlation function; STIT tessellation; Stochastic geometry; Variance asymptotic |
| Volume: | 25 |
| Issue: | Artikel 47 |
| First Page: | 47-1 |
| Last Page: | 47-28 |
| Note: | Dieser Beitrag ist auf Grund des DEAL-Springer-Vertrages frei zugänglich. |
| Dewey Decimal Classification: | Naturwissenschaften und Mathematik / Mathematik |
| open_access (DINI-Set): | open_access |
| faculties: | Fakultät für Mathematik |
| Licence (English): |  Creative Commons - CC BY 4.0 - Attribution 4.0 International |
