  Consider two independent random strings having same length and taking values
uniformly in a common finite alphabet. We study the order of the variance of
the length of the longest common subsequences (LCS) of these strings when long
blocks, or other types of atypical substrings, are sparsely added into one of
them. Under weak conditions on the derivative of the mean LCS-curve, the order
of the variance of the LCS is shown to be linear in the length of the strings.
We also argue that our proofs carry over to many models used by computational
biologists to simulate DNA-sequences. This is the first result where the open
question of the order of the fluctuation of the LCS of random strings is solved
for a realistic model. Until now, this type of result had only been established
for low entropy cases.
