  We study spatial clustering in a discrete, one-dimensional, stochastic, toy
model of heavy particles in turbulence and calculate the spectrum of
multifractal dimensions $D_q$ as functions of a dimensionless parameter,
$\alpha$, that plays the role of an inertia parameter. Using the fact that it
suffices to consider the linearized dynamics of the model at small separations,
we find that $D_q =D_2/(q-1)$ for $q=2,3,\ldots$. The correlation dimension
$D_2$ turns out to be a non-analytic function of the inertia parameter in this
model. We calculate $D_2$ for small $\alpha$ up to the next-to-leading order in
the non-analytic term.
