论文信息 - Longest convex chains

Longest convex chains

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

I. Bárány | G. Ambrus

[1] N. Enriquez. Convex chains in Z^2 , 2006 .

[2] I. Bárány,et al. On maximal convex lattice polygons inscribed in a plane convex set , 2006 .

[3] Noga Alon,et al. The Probabilistic Method, Second Edition , 2004 .

[4] Günter Rote,et al. A Central Limit Theorem for Convex Chains in the Square , 2000, Discret. Comput. Geom..

[5] Imre Brny. in Convex Position , 1999 .

[6] Imre Bárány,et al. Sylvester's question : The probability that n points are in convex position , 1999 .

[7] P. Diaconis,et al. Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem , 1999 .

[8] M. Talagrand. A new look at independence , 1996 .

[9] P. Valtr,et al. Probability thatn random points are in convex position , 1995, Discret. Comput. Geom..

[10] Noga Alon,et al. The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[11] B. Logan,et al. A Variational Problem for Random Young Tableaux , 1977 .

[12] A. Rényi,et al. über die konvexe Hülle von n zufällig gewählten Punkten , 1963 .