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arXiv · 1506.01495

Lipschitz partition processes

Harry Crane
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Abstract

We introduce a family of Markov processes on set partitions with a bounded number of blocks, called Lipschitz partition processes. We construct these processes explicitly by a Poisson point process on the space of Lipschitz continuous maps on partitions. By this construction, the Markovian consistency property is readily satisfied; that is, the finite restrictions of any Lipschitz partition process comprise a compatible collection of finite state space Markov chains. We further characterize the class of exchangeable Lipschitz partition processes by a novel set-valued matrix operation.

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Harry Crane. 2015-06-04. Lipschitz partition processes. https://doi.org/10.3150/14-bej607

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