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Fragmentation of ordered partitions and intervals. (English) Zbl 1109.60058

Summary: Fragmentation processes of exchangeable partitions have already been studied by several authors. This paper deals with fragmentations of exchangeable compositions, i.e. partitions of \(\mathbb N\) in which the order of the blocks matters. We will prove that such a fragmentation is bijectively associated to an interval fragmentation. Using this correspondence, we then study two examples: Ruelle’s interval fragmentation and the interval fragmentation derived from the standard additive coalescent.

MSC:

60J25 Continuous-time Markov processes on general state spaces
60G09 Exchangeability for stochastic processes
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