Longest convex chains

Details Longest convex chains Longest convex chains

2009-06-30

arxiv.org/abs/0906.5452v1

Mathematics

Probability

25 pages

Scientific paper

10.1002/rsa.20269

Assume $X_n$ is a random sample of $n$ uniform, independent points from a triangle $T$. The longest convex chain, $Y$, of $X_n$ is defined naturally. The length $|Y|$ of $Y$ is a random variable, denoted by $L_n$. In this article, we determine the order of magnitude of the expectation of $L_n$. We show further that $L_n$ is highly concentrated around its mean, and that the longest convex chains have a limit shape.

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