Random Lattices and Random Sphere Packings: Typical Properties
Abstract
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 $C(\nu).$
 Publication:

arXiv eprints
 Pub Date:
 November 2000
 arXiv:
 arXiv:mathph/0011040
 Bibcode:
 2000math.ph..11040S
 Keywords:

 Mathematical Physics;
 Combinatorics;
 82B05