The Annals of Probability

The cut-and-paste process

Harry Crane

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We characterize the class of exchangeable Feller processes evolving on partitions with boundedly many blocks. In continuous-time, the jump measure decomposes into two parts: a $\sigma$-finite measure on stochastic matrices and a collection of nonnegative real constants. This decomposition prompts a Lévy–Itô representation. In discrete-time, the evolution is described more simply by a product of independent, identically distributed random matrices.

Article information

Ann. Probab., Volume 42, Number 5 (2014), 1952-1979.

First available in Project Euclid: 29 August 2014

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Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60G09: Exchangeability 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]

Exchangeable random partition de Finetti’s theorem Lévy–Itô decomposition paintbox process coalescent process interacting particle system Feller process random matrix product


Crane, Harry. The cut-and-paste process. Ann. Probab. 42 (2014), no. 5, 1952--1979. doi:10.1214/14-AOP922.

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