Random lattices and random sphere packings: Typical properties (Q2732621)

The random quantity \(\Delta(\sigma)\) is considered, where \(\sigma\) is a typical random sphere packing and \(\Delta(\sigma)\) is the density of \(\sigma\). The authors firstly review the results on the typical lattice packings and show that the density is of order \(2^{-n}\). Then the corresponding problem for random (non-lattice) packings is investigated. In this case some ``improvement'' of the packing is needed and the resulting packings have densities of order \(C(\nu)2^{-n}\). The term \(C(\nu)\) is estimated as well.