Gibbs distributions for random partitions generated by a fragmentation process

  title={Gibbs distributions for random partitions generated by a fragmentation process},
  author={Nathanael Berestycki and Jim Pitman},
In this paper we study random partitions of {1, . . . , n} where every cluster of size j can be in any of wj possible internal states. The Gibbs (n, k, w) distribution is obtained by sampling uniformly among such partitions with k clusters. We provide conditions on the weight sequence w allowing construction of a partition valued random process where at step k the state has the Gibbs (n, k, w) distribution, so the partition is subject to irreversible fragmentation as time evolves. For a… CONTINUE READING
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