Correlation decay for hard spheres via Markov chains

We improve upon all known lower bounds on the critical fugacity and density of hard sphere model in dimensions three higher. As dimension tends to infinity, our improvements are by factors 2 1.7, respectively. make these utilizing techniques from theoretical computer science show that a certain Markov chain for sampling mixes rapidly at low enough fugacities. then prove an equivalence between optimal spatial temporal mixing spheres deduce results.