Abstract
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 no-
table 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 dis-
tribution. In these notes we survey recent developments of the theory of
regenerative partitions and compositions. In particular, we discuss connec-
tion between ordered and unordered structures, regenerative properties of
the Ewens-Pitman partitions, and asymptotics of the number of compo-
nents.
Original language | English |
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Pages (from-to) | 105-156 |
Number of pages | 52 |
Journal | Probability Surveys |
Volume | 7 |
DOIs | |
Publication status | Published - 2010 |