Abstract
We prove that the volumes determined by the lengths of the non-zero vectors ±x in a random lattice L of covolume 1 define a stochastic process that, as the dimension n tends to infinity, converges weakly to a Poisson process on the positive real line with intensity 1/2. This generalizes earlier results by Rogers (Proc Lond Math Soc (3) 6:305-320, 1956, Thm. 3) and Schmidt (Acta Math 102:159-224, 1959, Satz 10).
| Original language | English |
|---|---|
| Journal | Mathematische Zeitschrift |
| Volume | 269 |
| Issue number | 3-4 |
| Pages (from-to) | 945-954 |
| ISSN | 0025-5874 |
| Publication status | Published - Dec 2011 |