- Mutation processes such as point mutation, insertion, deletion, and duplication (including tandem and interspersed duplication) have an important role in evolution, as they lead to genomic diversity, and thus to phenotypic variation. In this work, we study the expressive power of interspersed duplication, i.e., its ability to generate diversity, via a simple but fundamental stochastic model, where the length and the location of the substring that is duplicated and the point of insertion of the copy are chosen randomly. We investigate the properties of the set of high-probability sequences in these stochastic systems. In particular we provide results regarding the asymptotic behavior of frequencies of symbols and strings in a sequence evolving through interspersed duplication. The study of such systems is an important step towards the design and analysis of more realistic and sophisticated models of genomic mutation processes.