We present a perfect simulation of the hard disks model via the partial rejection sampling method. Provided the density of disks is not too high, the method produces exact samples in $O(\log n)$ rounds, and total time $O(n)$, where $n$ is the expected number of disks. The method extends easily to the hard spheres model in $d>2$ dimensions. In order to apply the partial rejection method to this continuous setting, we provide an alternative perspective of its correctness and run-time analysis that is valid for general state spaces.

翻译：我们通过部分拒绝采样方法对硬盘模型进行完美的模拟。如果磁盘密度不高,该方法以美元(glog n) 圆环和总时间(n) 美元(n) 美元(美元) 生成精确样品,而美元(n) 是磁盘的预期数量。该方法很容易以$> 2 维度(d> $) 扩大到硬球模型。为了对这一连续环境应用部分拒绝方法,我们提供了另一种观点,说明其正确性和运行时间分析对一般州空间有效。