二元随机词最优对齐得分的方差及非对称得分函数
On the Variance of the Optimal Alignments Score for Binary Random Words and an Asymmetric Scoring Function
摘要：
我们研究了两个独立的具有相同长度的iid二进制随机字的最优比对得分的方差的顺序。字母是等概率的，但评分函数是这样的，一个字母的得分比另一个大。在这种情况下，我们证明了方差的顺序是线性的共同长度。最优对齐是最长公共连续性的推广，它们可以表示为具有相关权重的二维最后一次通过渗流环境中的最优路径。
英文摘要：
We investigate the order of the variance of the optimal alignments score of two independent iid binary random words having the same length. The letters are equiprobable, but the scoring function is such that one letter has a larger score than the other. In this setting, we prove that the order of variance is linear in the common length. Optimal alignments constitute a generalization of longest common subsequences, they can be represented as optimal paths in a two-dimensional last passage percolation setting with dependent weights.
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