  We consider the {\it concentration functions problem} for discrete quantum
groups; we prove that if $\mathbb{G}$ is a discrete quantum group, and $\mu$ is
an irreducible state in $l^1(\mathbb{G})$, then the convolution powers $\mu^n$,
considered as completely positive maps on $c_0(\mathbb{G})$, converge to zero
in strong operator topology.
