  We revisit, beyond the uniform case, some aspects of the convergence of the
cumulative shape of the RSK Young diagrams associated with random words,
obtaining rates of convergence in Kolmogorov's distance. Since the length of
the top row of the diagrams is the length of the longest increasing
subsequences of the word, a corresponding rate result follows. This is then
extended to the length of the longest common and increasing subsequences in two
or more random words.
