Leaves on the line and in the plane

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.

Random sequential covering

“…Our definition of the RSC is an analog of the RSA. Among other random coverings, we mention the procedure introduced by Matheron [57,58], known as visible confetti or the dead leaves model (DLM), see [59][60][61][62][63][64][65]. In this model, leaves fall at random onto the ground long enough, so the ground is completely covered.…”

Functional Central Limit Theorems for Local Statistics of Spatial Birth-Death Processes in the Thermodynamic Regime

“…Secondly, the model assumptions in [18] make it applicable only to scenarios with spatially uniform point density. More recently, functionals of random tessellations of the pure-birth processes (the "dead leaves" model) were shown to converge to Ornstein-Uhlenbeck process in [20].…”