Geometric decomposition of the $d$-dimensional hard-sphere partition function (opens in new tab)

We introduce a geometric decomposition of the hard-sphere partition function. Using a close-packing-inspired geometric bound on the available insertion volume, made rigorous when a corresponding local density certificate is available, we establish a reference upper bound $Q^\ast$ on the configurational integral. Factoring this upper bound out of the statistical geometric partition function of Speedy yields a new form for the $d$-dimensional part...