The Ewens process on spaces of even and balanced partitions

Details The Ewens process on spaces of even and balanced partitions The Ewens process on spaces of even and balanced partitions

2011-10-17

arxiv.org/abs/1110.3817v1

Mathematics

Statistics Theory

13 pages

Scientific paper

We discuss a generalization of the Ewens partition process to $\partitionsj$, the space of partitions whose block sizes are divisible by $j\in\mathbb{N}$, called even partitions of order $j$, or $j$-even partitions, and $\partitionsneut$, the subspace of $\partitionsj$ whose elements are labeled in $[j]$ and whose blocks contain an equal number of elements with each label, called $j$-balanced partitions. As in the Ewens process, these processes can be constructed sequentially according to a random seating rule. For both balanced and even partitions we can associate a projective system on which we construct random processes which project to the Chinese restaurant processes on the respective partition spaces.

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