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

Clément Deslandes; Christian Houdré

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arXiv · 2212.01630

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

Clément Deslandes·Christian Houdré

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Abstract

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.

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Clément Deslandes, Christian Houdré. 2022-12-03. On the rate of convergence of the shape of Young diagrams associated with random words. https://arxiv.org/abs/2212.01630

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