Random Lattices and Random Sphere Packings: Typical Properties

Details Random Lattices and Random Sphere Packings: Typical Properties Random Lattices and Random Sphere Packings: Typical Properties

2000-11-23

arxiv.org/abs/math-ph/0011040v1

Physics

Mathematical Physics

Scientific paper

We review results about the density of typical lattices in $R^n.$ They state
that such density is of the order of $2^{-n}.$ We then obtain similar results
for random packings in $R^n$: after taking suitably a fraction $\nu$ of a
typical random packing $\sigma$, the resulting packing $\tau$ has density
$C(\nu) 2^{-n},$ with a reasonable $C(\nu).$ We obtain estimates on $C(\nu).$

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