Random lattices and random sphere packings: Typical properties
type: Item
instance of: scholarly article
zbMATH Open document ID: 0999.11032
publication date: 2002-07-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/math-ph/0011040
Mathematics Subject Classification ID: 11H31
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 1624639
zbMATH Keywords: sphere packing
zbMATH Keywords: density
zbMATH Keywords: random field
author: S. B. Shlosman
author: Mikhail Anatolievich Tsfasman
MaRDI profile type: Publication
arXiv ID: math-ph/0011040
title: Random lattices and random sphere packings: Typical properties
published in: Moscow Mathematical Journal
review text: 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.
reviewed by: Peter Boyvalenkov
description: scientific article; zbMATH DE number 1624639