Perfect simulation of the hard disks model by partial rejection sampling

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.