  Among the discrete evolution equations describing a quantum system $\rH_S$
undergoing repeated quantum interactions with a chain of exterior systems, we
study and characterize those which are directed by classical random variables
in $\RR^N$. The characterization we obtain is entirely algebraical in terms of
the unitary operator driving the elementary interaction. We show that the
solutions of these equations are then random walks on the group $U(\rH_0)$ of
unitary operators on $\rH_0$.
