General approach to the fluctuations problem in random sequence comparison

Abstract

We present a general approach to the problem of determining the asymptotic order of the variance of the optimal score between two independent random sequences defined over an arbitrary finite alphabet. Our general approach is based on identifying random variables driving the fluctuations of the optimal score and conveniently choosing functions of them which exhibit certain monotonicity properties. We show how our general approach establishes a common theoretical background for the techniques used by Matzinger et al. in a series of previous articles [6, 8, 20, 24, 26, 37] studying the same problem in especial cases. Additionally, we explicitely apply our general approach to study the fluctuations of the optimal score between two random sequences over a finite alphabet (closing the study as initiated in [26]) and of the length of the longest common subsequences between two random sequences with a certain block structure (generalizing part of [37]).