  In this paper we consider the long time asymptotics of a linear version of
the Smoluchowski equation which describes the evolution of a tagged particle
moving at constant speed in a random distribution of fixed particles. The
volumes $v$ of the particles are independently distributed according to a
probability distribution which decays asymptotically as a power law
$v^{-\sigma}$. The validity of the equation has been rigorously proved in
\cite{NoV} for values of the exponent $\sigma>3$. The solutions of this
equation display a rich structure of different asymptotic behaviours according
to the different values of the exponent $\sigma$. Here we show that for
$\frac{5}{3}<\sigma<2$ the linear Smoluchowski equation is well posed and that
there exists a unique self-similar profile which is asymptotically stable.
