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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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https://hal.archives-ouvertes.fr/hal-01153127
Contributor : Jean-Christophe Breton <>
Submitted on : Saturday, May 23, 2015 - 1:49:32 PM
Last modification on : Monday, July 6, 2020 - 3:38:10 PM
Document(s) archivé(s) le : Thursday, April 20, 2017 - 2:35:18 AM

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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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