  For a residually finite group $G$, its normal subgroups $G\supset G_1\supset
G_2\cdots$ with $\cap_{n\in\mathbb N}G_n=\{e\}$ and for a growth function
$\gamma$ we construct a unitary representation $\pi_\gamma$ of $G$. For the
minimal growth, $\pi_\gamma$ is weakly equivalent to the regular
representation, and for the maximal growth it is weakly equivalent to the
direct sum of the quasiregular representations on the quotients $G/G_n$. In the
case of intermediate growth we show two examples of different behaviour of
$\pi_\gamma$.
