long blocks. As $n$ goes to infinity, the number of long blocks tends to infinity and their lengths are negligible when compared to $n$. This leads to our main result, Theorem \[distance\], which says that the distance between the two smallest (for the lexicographic order) long blocks, divided by the length $n$ of the word, follows asymptotically the uniform law on $[0,1]$. In section \[facteur\], we rephrase this result in terms of standard right factor and finally we generalize, in section \[section\_q\], the obtained results to the case of an alphabet with $q$ letters.

Random words and random Lyndon words {#words}
====================================

Let $\mathcal A=\{a,b\}$ be an ordered alphabet ($a<b$) and $\mathcal A^n$ be the set of all words with length $n$. If $w \in \mathcal A^n$, write $w=(w_1, \dots, w_n)$ and define: $$\tau w=(w_2,\dots, w_n,w_1).$$ Then $<\tau>=\{Id,\tau, \dots , \tau^{n-1}\}$ is the group of cyclic permutations of the letters of a word with length $n$. A word $w \in \mathcal A^n$ is called *primitive* if $$(\exists k \in \{0,1, \dots, n-1\} \mbox{ such that }\tau^kw=w)
\Rightarrow (k
=0).$$ Denote by $\mathcal P_n$ the set of primitive words in $\mathcal A^n$, by $\mathcal N_n$ its complement.

Remember that a Lyndon 