Results 1  10
of
14
PoissonDirichlet and GEM invariant distributions for splitandmerge transformations of an interval partition
, 2001
"... This paper introduces a splitandmerge transformation of interval partitions which combines some features of one model studied by Gnedin and Kerov [10, 11] and another studied by Tsilevich [30, 29] and MayerWolf, Zeitouni and Zerner [20]. The invariance under this splitandmerge transformatio ..."
Abstract

Cited by 49 (0 self)
 Add to MetaCart
This paper introduces a splitandmerge transformation of interval partitions which combines some features of one model studied by Gnedin and Kerov [10, 11] and another studied by Tsilevich [30, 29] and MayerWolf, Zeitouni and Zerner [20]. The invariance under this splitandmerge transformation of the interval partition generated by a suitable Poisson process yields a simple proof of the recent result of [20] that a PoissonDirichlet distribution is invariant for a closely related fragmentationcoagulation process. Uniqueness and convergence to the invariant measure are established for the splitandmerge transformation of interval partitions, but the corresponding problems for the fragmentationcoagulation process remain open.
Random Walks on Trees and Matchings
 Electron. J. Probab
, 2002
"... We give sharp rates of convergence for a natural Markov chain on the space of phylogenetic trees and dually for the natural random walk on the set of perfect matchings in the complete graph on 2n vertices. Roughly, the results show that n log n steps are necessary and su#ce to achieve randomness. ..."
Abstract

Cited by 24 (6 self)
 Add to MetaCart
We give sharp rates of convergence for a natural Markov chain on the space of phylogenetic trees and dually for the natural random walk on the set of perfect matchings in the complete graph on 2n vertices. Roughly, the results show that n log n steps are necessary and su#ce to achieve randomness. The proof depends on the representation theory of the symmetric group and a bijection between trees and matchings.
Gibbs distributions for random partitions generated by a fragmentation process
, 2006
"... process ..."
(Show Context)
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
Asymptotics for Logical Limit Laws: When the Growth of the Components is in an RT Class
 TRANS. AMER. MATH. SOC
, 2003
"... ... this paper we develop elementary techniques, based on a Tauberian theorem of Schur (as well as a modication of his theorem), that signicantly extend the classes of structures for which we know that Compton's theory can be applied. ..."
Abstract

Cited by 17 (3 self)
 Add to MetaCart
(Show Context)
... this paper we develop elementary techniques, based on a Tauberian theorem of Schur (as well as a modication of his theorem), that signicantly extend the classes of structures for which we know that Compton's theory can be applied.
Twoparameter PoissonDirichlet measures and reversible exchangeable fragmentationcoalescence processes
, 2007
"... ..."
Equilibrium for Fragmentation With Immigration
, 2005
"... This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a selfsimilar fragmentation. Criteria for existence and absence of stationary distributions are established and uniquenes ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a selfsimilar fragmentation. Criteria for existence and absence of stationary distributions are established and uniqueness is proved. Also, convergence rates to the stationary distribution are given. Linear equations which are the deterministic counterparts of fragmentation with immigration processes are next considered. As in the stochastic case, existence and uniqueness of solutions, as well as existence and uniqueness of stationary solutions, are investigated.
Compton's Method for Proving Logical Limit Laws
 CONTEMPORARY MATHEMATICS
, 2003
"... Developments in the study of logical limit laws for both labelled and unlabelled structures, based on the methods of Compton (1987/1989), are surveyed, and a sandwich theorem is proved for multiplicative systems. ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Developments in the study of logical limit laws for both labelled and unlabelled structures, based on the methods of Compton (1987/1989), are surveyed, and a sandwich theorem is proved for multiplicative systems.
Contents lists available at ScienceDirect Journal of Theoretical Biology
"... journal homepage: www.elsevier.com/locate/yjtbi ..."
(Show Context)