In high dimension, a rescaled typical Poisson-Voronoi cell converges to a shape with inradius 1/2, outradius 1, diameter and mean width 2, and its fixed-codimension faces are mostly microscopic, with an exponential count.
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On the shape of the typical Poisson-Voronoi cell in high dimensions
In high dimension, a rescaled typical Poisson-Voronoi cell converges to a shape with inradius 1/2, outradius 1, diameter and mean width 2, and its fixed-codimension faces are mostly microscopic, with an exponential count.