We give a unified simple proof of recent results of Alexander concerning the rate of convergence of the mean length of the longest common subsequence of two random sequences and the rate of convergence of the expected value of certain passage times in percolation theory.
"On Rates of Convergence for Common Subsequences and First Passage Time." Ann. Appl. Probab. 5 (1) 44 - 48, February, 1995. https://doi.org/10.1214/aoap/1177004827