  We show that a Calogero-Sutherland type model with anharmonic interactions of
fourth and sixth orders leads to the matrix model corresponding to the branched
polymers. We also show that by suitably modifying this model one can also
obtain N-particle problems which are connected to matrix models corresponding
to the pure gravity phase as well as corresponding to the transition point
between the soap bubble and the branched polymer phase.

Condensed Matter;High Energy Physics - Theory