The rate of the convergence of the mean score in random sequence comparison

Details The rate of the convergence of the mean score in random sequence comparison The rate of the convergence of the mean score in random sequence comparison

2010-11-11

arxiv.org/abs/1011.2688v3

Mathematics

Probability

13 pages, 1 figure

Scientific paper

We consider a general class of super-additive scores measuring the similarity of two independent sequences of $n$ i.i.d. letters from a finite alphabet. Our object of interest is the mean score by letter $l_n$. By the subadditivity $l_n$ is nondecreasing and converges to a limit $l$. We give a simple method of bounding the difference $l-l_n$ and obtaining the rate of convergence. Our result generalizes a previous result of Alexander, where only the special case of the longest common subsequence is considered.

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