We consider a general class of superadditive scores measuring the similarity of two independent sequences of n i.i.d. letters from a finite alphabet. Our object of interest is the mean score by letter ln. By subadditivity ln is nondecreasing and converges to a limit l. We give a simple method of bounding the difference l − ln and obtaining the rate of convergence. Our result generalizes the previous result of Alexander [Ann. Appl. Probab. 4 (1994) 1074–1082], where only the special case of the longest common subsequence was considered.
"The rate of the convergence of the mean score in random sequence comparison." Ann. Appl. Probab. 22 (3) 1046 - 1058, June 2012. https://doi.org/10.1214/11-AAP778