  We present a new approach to the statistics of the cosmic density field and
to the mass distribution of high-contrast structures, based on the formalism of
Cayley trees. Our approach includes in one random process both fluctuations and
interactions of the density perturbations. We connect tree-related quantities,
like the partition function or its generating function, to the mass
distribution. The Press \& Schechter mass function and the Smoluchowski kinetic
equation are naturally recovered as two limiting cases corresponding to
independent Gaussian fluctuations, and to aggregation of high-contrast
condensations, respectively. Numerical realizations of the complete random
process on the tree yield an excess of large-mass objects relative to the Press
\& Schechter function. When interactions are fully effective, a power-law
distribution with logarithmic slope -2 is generated.
