Open Access
2010 Regeneration in random combinatorial structures
Alexander V. Gnedin
Probab. Surveys 7: 105-156 (2010). DOI: 10.1214/10-PS163


Kingman’s theory of partition structures relates, via a natural sampling procedure, finite partitions to hypothetical infinite populations. Explicit formulas for distributions of such partitions are rare, the most notable exception being the Ewens sampling formula, and its two-parameter extension by Pitman. When one adds an extra structure to the partitions like a linear order on the set of blocks and regenerative properties, some representation theorems allow to get more precise information on the distribution. In these notes we survey recent developments of the theory of regenerative partitions and compositions. In particular, we discuss connection between ordered and unordered structures, regenerative properties of the Ewens-Pitman partitions, and asymptotics of the number of components.


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Alexander V. Gnedin. "Regeneration in random combinatorial structures." Probab. Surveys 7 105 - 156, 2010.


Published: 2010
First available in Project Euclid: 18 May 2010

zbMATH: 1204.60028
MathSciNet: MR2684164
Digital Object Identifier: 10.1214/10-PS163

Primary: 60C05 , 60G09

Keywords: exchangeability , Random partitions and compositions , regeneration

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.7 • 2010
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