The Mean Width of Circumscribed Random Polytopes Dedicated to Professor Tibor Bisztriczky on the occasion of his 60th birthday

For a given convex body K in Rd, 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.