  In this paper we improve the probabilistic approach to compositions of
Ehrenborg, Levin and Readdy by introducing a simpler but more general
probabilistic model. As consequence we get some new estimates on the behavior
of a uniform random permutation $\sigma$ having a fixed descent set. In
particular we show that independently of the shape of the descent set,
$\sigma(i)$ and $\sigma(j)$ become independent when $i-j$ tends to $+\infty$.
