  The adhesive dynamics of a one-dimensional aggregating gas of point particles
is rigorously described. The infinite hierarchy of kinetic equations for the
distributions of clusters of nearest neighbours is shown to be equivalent to a
system of two coupled equations for a large class of initial conditions. The
solution to these nonlinear equations is found by a direct construction of the
relevant probability distributions in the limit of a continuous initial mass
distribution. We show that those limiting distributions are identical to those
of the statistics of shocks in the Burgers turbulence. The analysis relies on a
mapping on a Brownian motion problem with parabolic constraints.
