We study a stochastic aggregation model for the assembly of the contractile ring from a broad band of nodes during cytokinesis in fission yeast. We found that bands of nodes condense into rings when the range of node interactions is larger than the width of the band. Wide bands are unstable to clump formation due to Poisson density fluctuations. We derive expressions for node kinetics and times for ring vs clump formation and test them using numerical simulations. These results suggest clump formation mechanisms in mutant cells.