Results 1 
7 of
7
Gibbs distributions for random partitions generated by a fragmentation process
, 2006
"... process ..."
Ranked fragmentations
 ESAIM P&S
"... distributions for random partitions generated by a ..."
Abstract

Cited by 20 (3 self)
 Add to MetaCart
(Show Context)
distributions for random partitions generated by a
Regeneration in Random Combinatorial Structures
, 2009
"... Theory of Kingman’s partition structures has two culminating points • the general paintbox representation, relating finite partitions to hypothetical infinite populations via a natural sampling procedure, • a central example of the theory: the EwensPitman twoparameter partitions. In these notes we ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
(Show Context)
Theory of Kingman’s partition structures has two culminating points • the general paintbox representation, relating finite partitions to hypothetical infinite populations via a natural sampling procedure, • a central example of the theory: the EwensPitman twoparameter partitions. In these notes we further develop the theory by • passing to structures enriched by the order on the collection of categories, • extending the class of tractable models by exploring the idea of regeneration, • analysing regenerative properties of the EwensPitman partitions, • studying asymptotic features of the regenerative compositions.
The chain records
 Elec. J. Probab
, 2007
"... Abstract Chain records is a new type of multidimensional record. We discuss how often the chain records occur when the background sampling is from the unit cube with uniform distribution (or, more generally, from an arbitrary continuous product distribution in d dimensions). Extensions are given fo ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract Chain records is a new type of multidimensional record. We discuss how often the chain records occur when the background sampling is from the unit cube with uniform distribution (or, more generally, from an arbitrary continuous product distribution in d dimensions). Extensions are given for sampling from more general spaces with a selfsimilarity property.
Elect. Comm. in Probab. 13 (2008), 461–474 ELECTRONIC COMMUNICATIONS in PROBABILITY FRAGMENTING RANDOM PERMUTATIONS
, 2007
"... process Problem 1.5.7 from Pitman’s SaintFlour lecture notes [11]: Does there exist for each n a fragmentation process (Πn,k, 1 ≤ k ≤ n) such that Πn,k is distributed like the partition generated by cycles of a uniform random permutation of {1, 2,..., n} conditioned to have k cycles? We show that t ..."
Abstract
 Add to MetaCart
(Show Context)
process Problem 1.5.7 from Pitman’s SaintFlour lecture notes [11]: Does there exist for each n a fragmentation process (Πn,k, 1 ≤ k ≤ n) such that Πn,k is distributed like the partition generated by cycles of a uniform random permutation of {1, 2,..., n} conditioned to have k cycles? We show that the answer is yes. We also give a partial extension to general exchangeable Gibbs partitions. 1
Corners and Records of the Poisson Process in Quadrant
, 2007
"... The scaleinvariant spacings lemma due to Arratia, Barbour and Tavaré establishes the distributional identity of a selfsimilar Poisson process and the set of spacings between the points of this process. In this note we connect this result with properties of a certain set of extreme points of the un ..."
Abstract
 Add to MetaCart
(Show Context)
The scaleinvariant spacings lemma due to Arratia, Barbour and Tavaré establishes the distributional identity of a selfsimilar Poisson process and the set of spacings between the points of this process. In this note we connect this result with properties of a certain set of extreme points of the unit Poisson process in the positive quadrant.
Poisson Dirichlet(α, θ)Bridge Equations and CoagulationFragmentation Duality
, 2009
"... This paper derives distributional properties of a class of exchangeable bridges closely related to the PoissonDirichlet (α, θ) family of bridges. We then show that various stochastic equations derived for these bridges lead to constructions of a new large class of coagulation and fragmentation oper ..."
Abstract
 Add to MetaCart
This paper derives distributional properties of a class of exchangeable bridges closely related to the PoissonDirichlet (α, θ) family of bridges. We then show that various stochastic equations derived for these bridges lead to constructions of a new large class of coagulation and fragmentation operators that satisfy a duality property, and are otherwise easily manipulated. This class, builds on, and includes the duality relations developed in Pitman (15), Bertoin and Goldschmidt (2), and Dong, Goldschmidt and Martin (4), which we can treat in a unified way. Our exposition also suggests an approach to obtain other dualities and related results.