%0 Journal Article %T Asymptotic volume in Hilbert Geometries %A Constantin Vernicos %J Mathematics %D 2012 %I arXiv %X We prove that the metric balls of a Hilbert geometry admit a volume growth at least polynomial of degree their dimension. We also characterise the convex polytopes as those having exactly polynomial volume growth of degree their dimension. %U http://arxiv.org/abs/1207.1142v1