Algorithms for Hard-Constraint Point Processes via Discretization

We study the algorithmic applications of a natural discretization for hard-sphere model and Widom–Rowlinson in region $$d $$ -dimensional Euclidean space \mathbb {V} \subset {R} ^{d}$$ . These continuous models are frequently used statistical physics to describe mixtures one or multiple particle types subjected hard-core interactions. For each type, particles distributed according Poisson point process with type-specific activity parameter, called fugacity. The Gibbs distribution over all possible system states is characterized by mixture these processes conditioned that no two closer than some type-dependent distance threshold. A key part better understanding its normalizing constant, partition function. Our main result first deterministic approximation algorithm function box-shaped regions space. algorithms have quasi-polynomial running time volume $$\nu \left( \right) if fugacity below certain unit volume, this threshold $$\textrm{e}/2^d As number dimensions increases, bound asymptotically matches best known results randomized prove similar bounds model. To our knowledge, rigorous