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

On the rate of convergence of the shape of Young diagrams associated with random words