The Chen-Stein method of Poisson approximation has been used to establish theorems about comparison of two DNA or protein sequences. The most useful result for sequence alignment applies to alignment scoring with no gaps. However, there has not been a valid method to assign statistical significance to alignment scores with gaps. In this paper we extend Poisson approximation techniques using the Aldous clumping heuristic to a practical method of estimating statistical significance.
"Sequence Comparison Significance and Poisson Approximation." Statist. Sci. 9 (3) 367 - 381, August, 1994. https://doi.org/10.1214/ss/1177010382