Longest convex chains TeX Export

@article{citeulike:5034468, abstract = {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.}, archivePrefix = {arXiv}, author = {Ambrus, Gergely and Barany, Imre}, citeulike-article-id = {5034468}, citeulike-linkout-0 = {http://arxiv.org/abs/0906.5452}, citeulike-linkout-1 = {http://arxiv.org/pdf/0906.5452}, eprint = {0906.5452}, keywords = {2d, convex, probability}, month = {Jun}, posted-at = {2009-07-01 17:11:52}, priority = {2}, title = {Longest convex chains}, url = {http://arxiv.org/abs/0906.5452}, year = {2009} }

TY - JOUR ID - citeulike:5034468 L3 - citeulike-article-id:5034468 N2 - 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. TI - Longest convex chains KW - 2d KW - convex KW - probability AU - Ambrus, Gergely AU - Barany, Imre PY - 2009/Jun/30/ UR - http://arxiv.org/abs/0906.5452 ER -