On the variance of the mean width of random polytopes circumscribed around a convex body

Abstract Let be a convex body in in which a ball rolls freely and which slides freely in a ball. Let be the intersection of i.i.d. random half‐spaces containing chosen according to a certain prescribed probability distribution. We prove an asymptotic upper bound on the variance of the mean width of as . We achieve this result by first proving an asymptotic upper bound on the variance of the weighted volume of random polytopes generated by i.i.d. random points selected according to certain probability distributions, then, using polarity, we transfer this to the circumscribed model.