Generating Functionals of Random Packing Point Processes: From Hard-Core to Carrier Sensing

Stabilization and limit theorems for geometric functionals of Gibbs point processes

Given a Gibbs point process P on R having a weak enough potential Ψ, we consider the random measures μλ := P x∈P∩Qλ ξ(x,P ∩Qλ)δx/λ1/d , where Qλ := [−λ /2, λ/2] is the volume λ cube and where ξ(·, ·) is a translation invariant stabilizing functional. Subject to Ψ satisfying a localization property and translation invariance, we establish weak laws of large numbers for λ−1μλ(f), f a bounded test...

On the Generating Functionals of a Class of Random Packing Point Processes

Large deviations for functionals of spatial point processes with applications to random packing and spatial graphs

Functionals of spatial point process often satisfy a weak spatial dependence condition known as stabilization. We prove general Donsker–Varadhan large deviation principles (LDP) for such functionals and show that the general result can be applied to prove LDPs for various particular functionals, including those concerned with random packing, nearest neighbor graphs, and lattice versions of the ...

Perfect simulation and moment properties for the Matérn Type III Process

The Matérn type III hard core point process (shortly Matérn III process) is a less well-known but for many applications more appealing or realistic model than the Matérn type I and II hard core point processes. This paper focuses on the stationary (and hence infinite) Matérn III process from a probabilistic and a stochastic geometry perspective. Briefly, given a hard core parameter R > 0, the M...

A Hard Convex Core Yukawa Equation of State for Nonassociated Chain Molecules

The compressibility factor of nonassociated chain molecules composed of hard convex core Yukawa segments was derived with SAFT-VR and an extension of the Barker-Henderson perturbation theory for convex bodies. The temperature-dependent chain and dispersion compressibility factors were derived using the Yukawa potential. The effects of temperature, packing fraction, and segment number on the com...