Stochastic reverse isoperimetric inequalities in the plane.

In recent years, it has been shown that some classical inequalities follow from a local stochastic dominance for naturally associated random polytopes. We strengthen planar isoperimetric inequalities by attaching a stochastic model to some classical inequalities, such as Mahler's Theorem, and a reverse Lutwak–Zhang inequality, the polar for L p centroid bodies. In particular, we obtain the dual counterpart to a result of Bisztriczky–Böröczky. [ABSTRACT FROM AUTHOR]