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. \\
Original languageEnglish
Article number53
Pages (from-to)1-40
Number of pages40
JournalElectronic Journal of Probability
Volume25
Publication statusPublished - 5 May 2020

Keywords

  • random tessellation, dead leaves model, random measure, central limit theorem, Ornstein-Uhlenbeck process.

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