The mean width of circumscribed random polytopes

2009/01/21 by Böröczky, Károly J., Schneider, Rolf
#52A22 #FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.0901.3343

Abstract

For a given convex body K in R^d, a random polytope K⁽ⁿ⁾ is defined (essentially) as the intersection of n independent closed halfspaces containing K and having an isotropic and (in a specified sense) uniform distribution. We prove upper and lower bounds, of optimal orders, for the difference of the mean widths of K⁽ⁿ⁾ and K, as n tends to infinity. For a simplicial polytope P, a precise asymptotic formula for the difference of the mean widths of P⁽ⁿ⁾ and P is obtained.

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