We provide a perfect sampling algorithm for the hard-sphere model on subsets of $\mathbb{R}^d$ with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling algorithms have been devised to sample from the hard-sphere model, and our perfect sampling algorithm is efficient for a range of parameters for which only efficient approximate samplers were previously known and is faster than these known approximate approaches. Our methods also extend to the more general setting of Gibbs point processes interacting via finite-range, repulsive potentials.

翻译：我们提出了一种在$\mathbb{R}^d$子集上对硬球模型进行完美采样的算法，在强空间混合假设下，其期望运行时间与体积呈线性关系。已有大量完美采样和近似采样算法被设计用于对硬球模型进行采样，而我们的完美采样算法在参数范围内是高效的——此前在该范围内仅存在高效的近似采样器——并且其速度优于这些已知的近似方法。我们的方法还可推广至通过有限程排斥势相互作用的一般吉布斯点过程。