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Rapport Année : 2014

A Central Limit Theorem for the Length of the Longest Common Subsequence in Random Words

Christian Houdre
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Ümit Islak
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Résumé

Let (X_k )_{k≥1} and (Y_k )_{k≥1} be two independent sequences of independent identically distributed random variables having the same law and taking their values in a finite alphabet. Let LCn be the length of longest common subsequences in the two random words X_1 * * * X_n and Y_1 * * * Y_n . Under assumptions on the distribution of X1 , LC_n is shown to satisfy a central limit theorem. This is in contrast to the limiting distribution of the length of longest common subsequences in two independent uniform random permutations of {1, . . . , n}, which is shown to be the Tracy-Widom distribution.
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Dates et versions

hal-01064142 , version 1 (15-09-2014)

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  • HAL Id : hal-01064142 , version 1

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Christian Houdre, Ümit Islak. A Central Limit Theorem for the Length of the Longest Common Subsequence in Random Words. 2014. ⟨hal-01064142⟩
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