On the Rate of Approximation in Finite-Alphabet Longest Increasing Subsequence Problems

Details On the Rate of Approximation in Finite-Alphabet Longest Increasing Subsequence Problems On the Rate of Approximation in Finite-Alphabet Longest Increasing Subsequence Problems

2009-11-25

arxiv.org/abs/0911.4917v2

Mathematics

Probability

To Appear: Annals of Applied Probability

Scientific paper

The rate of convergence of the distribution of the length of the longest
increasing subsequence, towards the maximum eigenvalue of certain matrix
ensemble, is investigated. For finite-alphabet uniform and non-uniform iid
sources, a rate of $\log n /\sqrt{n}$ is obtained. The uniform binary case is
further explored, and an improved $1/\sqrt{n}$ rate obtained.

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