Distribution of Aligned Letter Pairs in Optimal Alignments of Random Sequences

Report

Considering the optimal alignment of two i.i.d. random sequences of length $n$, we show that when the scoring function is chosen randomly, almost surely the empirical distribution of aligned letter pairs in all optimal alignments converges to a unique limiting distribution as $n$ tends to infinity. This result is interesting because it helps understanding the microscopic path structure of a special type of last passage percolation problem with correlated weights, an area of long-standing open problems. Characterizing the microscopic path structure yields furthermore a robust alternative to optimal alignment scores for testing the relatedness of genetic sequences.

Authors: Hauser, R; Matzinger, H

• Publisher: Annals of Probability
• Publication date: 2012-11-01