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, 2017, 127 (5), pp.1676-1720. <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 : mardi 4 avril 2017 - 14:10:16
Document(s) archivé(s) le : jeudi 20 avril 2017 - 02:35:18

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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, 2017, 127 (5), pp.1676-1720. <10.1016/j.spa.2016.09.005>. <hal-01153127>

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