We study computational aspects of repulsive Gibbs point processes, which are probabilistic models of interacting particles in a finite-volume region of space. We introduce an approach for reducing a Gibbs point process to the hard-core model, a well-studied discrete spin system. Given an instance of such a point process, our reduction generates a random graph drawn from a natural geometric model. We show that the partition function of a hard-core model on graphs generated by the geometric model concentrates around the partition function of the Gibbs point process. Our reduction allows us to use a broad range of algorithms developed for the hard-core model to sample from the Gibbs point process and approximate its partition function. This is, to the extend of our knowledge, the first approach that deals with pair potentials of unbounded range. We compare the resulting algorithms with recently established results and study further properties of the random geometric graphs with respect to the hard-core model.

翻译：我们研究了排斥吉布斯点过程的计算问题，这类模型描述了有限空间区域内相互作用的粒子的概率行为。我们提出了一种将吉布斯点过程转化为硬核模型（一种被广泛研究的离散自旋系统）的方法。给定一个点过程实例，我们的转化会生成一个服从自然几何模型的随机图。我们证明，由该几何模型生成的图上的硬核模型配分函数，会围绕吉布斯点过程的配分函数呈集中趋势。这一转化使我们能够利用硬核模型领域的大量算法来对吉布斯点过程进行采样，并近似计算其配分函数。据我们所知，这是首个处理无界范围对势的方法。我们将所得算法与近期成果进行了比较，并进一步研究了此类随机几何图相对于硬核模型的性质。