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

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 نشر من قبل Jean-Christophe Breton
 تاريخ النشر 2015
  مجال البحث
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Let $X=(X_i)_{ige 1}$ and $Y=(Y_i)_{ige 1}$ 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 $X_1cdots X_n$ and $Y_1cdots Y_n$. 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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