Open Access
June 2012 The rate of the convergence of the mean score in random sequence comparison
Jüri Lember, Heinrich Matzinger, Felipe Torres
Ann. Appl. Probab. 22(3): 1046-1058 (June 2012). DOI: 10.1214/11-AAP778


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 lln 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.


Download Citation

Jüri Lember. Heinrich Matzinger. Felipe Torres. "The rate of the convergence of the mean score in random sequence comparison." Ann. Appl. Probab. 22 (3) 1046 - 1058, June 2012.


Published: June 2012
First available in Project Euclid: 18 May 2012

zbMATH: 1244.60095
MathSciNet: MR2977985
Digital Object Identifier: 10.1214/11-AAP778

Primary: 41A25 , 60C05 , 60K35

Keywords: longest common sequence , Random sequence comparison , rate of convergence

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.22 • No. 3 • June 2012
Back to Top