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This article is cited in 5 scientific papers (total in 5 papers)
Random lattices and random sphere packings: typical properties
S. Shlosmanab, M. A. Tsfasmanbcd a CNRS – Center of Theoretical Physics
b Institute for Information Transmission Problems, Russian Academy of Sciences
c Institut de Mathématiques de Luminy
d Independent University of Moscow
Abstract:
We review results about the density of typical lattices in $\mathbb R^n$. This density is of the order of $2^{-n}$. We then obtain similar results for random (non-lattice) sphere packings in $\mathbb R^n$: after suitably taking a fraction $\nu$ of centers of spheres in a typical random packing $\sigma$, the resulting packing $\tau$ has density $C(\nu) 2^{-n}$ with a reasonable $C(\nu)$. We obtain estimates of $C(\nu)$.
Key words and phrases:
Geometric density, random field, vertex covering number, sphere packing.
Received: September 1, 2000; in revised form January 30, 2001
Citation:
S. Shlosman, M. A. Tsfasman, “Random lattices and random sphere packings: typical properties”, Mosc. Math. J., 1:1 (2001), 73–89
Linking options:
https://www.mathnet.ru/eng/mmj13 https://www.mathnet.ru/eng/mmj/v1/i1/p73
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Abstract page: | 380 | References: | 67 |
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