Assume Xn is a random sample of n uniform, independent points from a triangle T. The longest convex chain, Y, of Xn is defined naturally (see the next paragraph). The length |Y| of Y is a random variable, denoted by Ln. In this article, we determine the order of magnitude of the expectation of Ln. We show further that Ln is highly concentrated around its mean, and that the longest convex chains have a limit shape. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009
['Gergely Ambrus', 'Imre Bárány']
Longest convex chains