For Poisson hyperplane K-cells, the expected mean width excess is between n^{-1} log^{d-1} n and n^{-2/(d+1)}, with exact limits for smooth bodies and simplicial polytopes.
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Poisson hyperplane processes and approximation of convex bodies
For Poisson hyperplane K-cells, the expected mean width excess is between n^{-1} log^{d-1} n and n^{-2/(d+1)}, with exact limits for smooth bodies and simplicial polytopes.