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

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.