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Random lattices and random sphere packings: Typical properties. (English) Zbl 0999.11032
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.

MSC:
11H31 Lattice packing and covering (number-theoretic aspects)
52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
82B05 Classical equilibrium statistical mechanics (general)
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