For each n>0, the Ewens sampling formula from population genetics is a measure on the set of all partitions of the integer n, To determine the limiting distributions for the part sizes of a partition with respect to the measures given by this formula, the paper associates to each partition a step function on [0,1]. Each jump in the function equals the number of parts in the partition of a certain size. The paper normalizes these functions and shows that the induced measures on D[0,1] converge to Wiener measure. This result complements Kingman’s frequency limit theorem for the Ewens partition structure.
