# On the Poisson distribution of lengths of lattice vectors in a random lattice - Mathematics > Number Theory

On the Poisson distribution of lengths of lattice vectors in a random lattice - Mathematics > Number Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: 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 processthat, as the dimension n tends to infinity, converges weakly to a Poissonprocess on the positive real line with intensity 1-2. This generalizes earlierresults by Rogers and Schmidt.

Author: ** Anders SÃ¶dergren**

Source: https://arxiv.org/