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Second-Order Properties for Planar Mondrian Tessellations

Author

Listed:
  • Carina Betken

    (Ruhr University Bochum)

  • Tom Kaufmann

    (Ruhr University Bochum)

  • Kathrin Meier

    (Ruhr University Bochum)

  • Christoph Thäle

    (Ruhr University Bochum)

Abstract

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.

Suggested Citation

  • Carina Betken & Tom Kaufmann & Kathrin Meier & Christoph Thäle, 2023. "Second-Order Properties for Planar Mondrian Tessellations," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-28, June.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10017-2
    DOI: 10.1007/s11009-023-10017-2
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