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.