Abstract
We investigate the order of the r-th, 1 ≤ r < +∞, central moment of the length of the longest common subsequences of two independent random words of size n whose letters are identically distributed and independently drawn from a finite alphabet. When all but one of the letters are drawn with small probabilities, which depend on the size of the alphabet, a lower bound is shown to be of order n r∕2. This result complements a generic upper bound also of order n r∕2.
Mathematics Subject Classification (2010). 60K35; 60C05; 05A05
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Acknowledgements
Many thanks to Ruoting Gong and an anonymous referee for their detailed reading and numerous comments on this paper.
This work was supported in part by the grant #246283 from the Simons Foundation and by a Simons Foundation Fellowship, grant #267336. Many thanks to the Laboratoire MAS of the École Centrale Paris and to the LPMA of the Université Pierre et Marie Curie (Paris VI) for their hospitality and support while part of this research was carried out.
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Houdré, C., Ma, J. (2016). On the Order of the Central Moments of the Length of the Longest Common Subsequences in Random Words. In: Houdré, C., Mason, D., Reynaud-Bouret, P., Rosiński, J. (eds) High Dimensional Probability VII. Progress in Probability, vol 71. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-40519-3_5
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DOI: https://doi.org/10.1007/978-3-319-40519-3_5
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