On the Poisson distribution of lengths of lattice vectors in a random lattice

Details On the Poisson distribution of lengths of lattice vectors in a random lattice On the Poisson distribution of lengths of lattice vectors in a random lattice

2010-01-20

arxiv.org/abs/1001.3623v2

Mathematische Zeitschrift 269 (2011) 945-954

Mathematics

Number Theory

9 pages; revised statement of Proposition 3

Scientific paper

We prove that the volumes determined by the lengths of the non-zero vectors
$\pm\vecx$ 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 and Schmidt.

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