On the limiting law of the length of the longest common and increasing subsequences in random words

Abstract : Let $X=(X_i)_{i\ge 1}$ and $Y=(Y_i)_{i\ge 1}$ be two sequences of independent and identically distributed (iid) random variables taking their values, uniformly, in a common totally ordered finite alphabet. Let LCI_$n$ be the length of the longest common and (weakly) increasing subsequence of $X_1\cdots X_n$ and $Y_1\cdots Y_n$. As $n$ grows without bound, and when properly centered and normalized, LCI$_n$ is shown to converge, in distribution, towards a Brownian functional that we identify.
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Stochastic Processes and their Applications, Elsevier, 2016, <10.1016/j.spa.2016.09.005>
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Contributeur : Jean-Christophe Breton <>
Soumis le : samedi 23 mai 2015 - 13:49:32
Dernière modification le : jeudi 23 février 2017 - 14:07:13

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Jean-Christophe Breton, Christian Houdré. On the limiting law of the length of the longest common and increasing subsequences in random words. Stochastic Processes and their Applications, Elsevier, 2016, <10.1016/j.spa.2016.09.005>. <hal-01153127>

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