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• W1555895414 abstract "The problem of the order of the uctuation of the Longest Common Subsequence (LCS) of two independent sequences has been open for decades. There exist contradicting conjectures [8], [4] on the topic. Lember and Matzinger [17] showed that with i.i.d. binary strings, the standard deviation is asymptotically linear in the length of the strings provided that 0 and 1 have very dierent probabilities. Nonetheless, with two i.i.d. sequences and a nite number of equiprobable colors the typical size of the uctuation remains unknown. A contiguous substring consisting only of one type of symbol is called block. For i.i.d. sequences with equiprobable symbols the blocks are independent of each other. In the present article, we determine the order of the uctuation of the LCS, for a special model of i.i.d. blocks. For achieving this goal, we developed a method which allows to reformulate the uctuation problem as (relatively) low dimensional optimization problem. The model we consider here is with three equiproble block lengths. The method can be applied to any other case including i.i.d. sequences, only that the optimization problem might be more complicated. The LCS problem can be formulated as a last passage percolation problem with correlated weights. The problem of the" @default.
• W1555895414 created "2016-06-24" @default.
• W1555895414 creator A5055560808 @default.
• W1555895414 creator A5071835517 @default.
• W1555895414 date "2010-01-08" @default.
• W1555895414 modified "2023-09-27" @default.
• W1555895414 title "Fluctuations of the Longest Common Subsequence for Sequences of Independent Blocks" @default.
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• W1555895414 hasPublicationYear "2010" @default.
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