Random sequential adsorption: Relationship to dead leaves and characterization of variability (Q5928032)

The authors describe new constructions for the planar unbounded random sequential absorption (RSA) model. The first construction defines the RSA model as the limit of a spatial birth process, while the second construction refers to the limit of a thinning scheme applied to a point process with points \((x,t,r)\) representing respectively the location, time and the radius of a disk placed at \(x\). It is assumed that \((x,t)\) forms a Poisson process on \(R^2\times [0,\infty)\) of unit intensity. These constructions allow for a direct comparison with Matheron's ``dead leaves'' model. In particular, the system of intact disks of the dead leaves model is a homogeneous and isotropic subsystem of the RSA model. For the case of disks with random radii the problem of statistical determination of the proposal radii distribution is discussed. Finally, second-order characteristics related to the pair correlation function are suggested for describing the variability of the RSA disk systems.