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A RANDOM CLUSTERING PROCESS

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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.

**Source**
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