Limit law of the standard right factor of a random Lyndon word

Regine Marchand (1) , Elahe Zohoorian Azad (1)

1 IECN - Institut Élie Cartan de Nancy

Consider the set of finite words on a totally ordered alphabet with $q$ letters. We prove that the distribution of the length of the standard right factor of a random Lyndon word with length $n$, divided by $n$, converges to: $$\mu(dx)=\frac1q \delta_{1}(dx) + \frac{q-1}q \mathbf{1}_{[0,1)}(x)dx,$$ when $n$ goes to infinity. The convergence of all moments follows. This paper completes thus the results of~\cite{Bassino}, giving the asymptotics of the mean length of the standard right factor of a random Lyndon word with length $n$ in the case of a two letters alphabet.

Domaines: Probabilités [math.PR]

Regine Marchand, Elahe Zohoorian Azad. Limit law of the standard right factor of a random Lyndon word. Combinatorics, Probability and Computing, 2007, 16, pp.417-434. ⟨hal-00002167⟩