论文标题
使用随机图来采样具有任意范围电势的排斥吉布斯点过程
Using random graphs to sample repulsive Gibbs point processes with arbitrary-range potentials
论文作者
论文摘要
我们研究了排斥吉布斯点过程的计算方面，这些过程是在有限体积的空间区域中相互作用颗粒的概率模型。我们介绍了一种将Gibbs点过程减少到硬核模型的方法，这是一个经过良好研究的离散旋转系统。给定这样一个点过程的实例，我们的还原生成了从天然几何模型绘制的随机图。我们表明，在Gibbs点过程的分区函数周围生成的图形上，硬核模型的分区函数集中在图表上。我们的还原使我们能够使用为硬核模型开发的广泛算法从Gibbs点过程中进行采样并近似其分区函数。这是我们知识的扩展，是第一种处理无限范围的配对电位的方法。我们将所得算法与最近确定的结果进行了比较，并研究了相对于硬核模型的随机几何图的进一步性能。
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.
