A RANDOM CLUSTERING PROCESS

MASAAKI SIBUYA

Department of Mathematics, Keio University, Hiyoshi, Yokohama 223, Japan

(Received December 26, 1991; revised August 25, 1992)

Abstract. A clustering process which generates simple and uniform random partitions is studied. It has a single parameter and generates, for a special value of the parameter, the partition of a random permutation into its cycles. The limit distribution of the size index of the generated partition is the joint of the independent Poisson distributions with means determined by the size and the parameter.

Key words and phrases: Bell polynomial, cycles of random permutation, Poisson approximation, Pólya urn model, Stirling number of the first kind.