Analysis of perfect sampling methods for hard-sphere models

We consider the problem of generating perfect samples from a Gibbs point process, a spatial process that is absolutely continuous w.r.t. a Poisson point process. Examples include area-interaction processes, hard-sphere models and Strauss processes. Traditionally, this is addressed using coupling from the past (CFTP) based methods. We consider acceptance-rejection methods that, unlike the common CFTP methods, do not have the impatient-user bias. Our key contribution is a novel importance sampling based acceptance-rejection methodology for generating perfect samples from Gibbs point processes. We focus on a simpler setting of hard-sphere models in a d-dimensional hypercube that we analyze in an asymptotic regime where the number of spheres generated increases to infinity while the sphere radius decreases to zero at varying rates.