Leaves on the line and in the plane

Mathew D. Penrose

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arXiv · 1806.03696

Leaves on the line and in the plane

Mathew D. Penrose

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Abstract

The Dead Leaves Model (DLM) provides a random tessellation of $d$-space, representing the visible portions of fallen leaves on the ground when $d=2$. For $d=1$, we establish formulae for the intensity, two-point correlations, and asymptotic covariances for the point process of cell boundaries, along with a functional CLT. For $d=2$ we establish analogous results for the random surface measure of cell boundaries, and also determine the intensity of cells in a more general setting than in earlier work of Cowan and Tsang. We introduce a general notion of Dead Leaves Random Measures and give formulae for means, asymptotic variances and functional CLTs for these measures; this has applications to various other quantities associated with the DLM.

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Mathew D. Penrose. 2018-06-10. Leaves on the line and in the plane. https://arxiv.org/abs/1806.03696

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