  Considering two optimally aligned random sequences, we investigate the effect
on the alignment score caused by changing a random letter in one of the two
sequences. Using this idea in conjunction with large deviations theory, we show
that in alignments with a low proportion of gaps the optimal alignment is
locally unique in most places with high probability. This has implications in
the design of recently pioneered alignment methods that use the local
uniqueness as a homology indicator.
