Asymptotic behavior of some factorizations of random words

In this paper, we consider the normalized lengths of factors some factorizations random words. First, for Lyndon factorization finite words with n independent letters drawn from a or infinite totally ordered alphabet according to general probability distribution, prove that limit law smallest is variant stickbreaking process. Convergence distribution longest Poisson–Dirichlet follows. Second, standard word: length right factor n-letters long word, derived such an alphabet, converges, when large, to: in which denotes letter alphabet.