Proof of David Kendall's conjecture concerning the shape of large random polygons
Let \(m(\omega)\) be a Poisson line process in the plane \(R^2\). The paper considers the tessellation of \(R^2\) into random polygons generated by \(m(\omega)\). ``Crofton cell'' \(K\) is the polygon which contains fixed point \(O\). \(A(K)\) is the area of \(K\). The main result: The shape \(\sigma(K)\) of a typical random polygon \(K\) of a large area is close to that of a disc (\(A(K)\to + \infty\)). For the entire collection see \textit{R. E. Miles} [Adv. Appl. Probab. 27, No. 2, 397-417 (1995; Zbl 0829.60008)].
scientific article; zbMATH DE number 1262968