A Calogero-Sutherland type model for branched polymers

We show that a Calogero-Sutherland type model with anharmonic interactions of fourth and sixth orders leads to the matrix model corresponding to 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