Large deviations for a triangular array of exchangeable random variables
Large deviations for exchangeable observations with applications.
Martingale problems for conditional distributions of Markov processes.
Noncommutative independence in the infinite braid and symmetric group
This is an introductory paper about our recent merge of a noncommutative de Finetti type result with representations of the infinite braid and symmetric group which allows us to derive factorization properties from symmetries. We explain some of the main ideas of this approach and work out a constructive procedure to use in applications. Finally we illustrate the method by applying it to the theory of group characters.
On exchangeable random variables and the statistics of large graphs and hypergraphs.
On the convergence of the ensemble Kalman filter
Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, the continuous mapping theorem gives convergence in probability of the ensemble members, and bounds on the ensemble then give convergence.
On the equivalence of some eternal additive coalescents
In this paper, we study additive coalescents. Using their representation as fragmentation processes, we prove that the law of a large class of eternal additive coalescents is absolutely continuous with respect to the law of the standard additive coalescent on any bounded time interval.
On the tail estimation of the norm of Rademacher sums.
Path transformations of first passage bridges.
Quasi-invariant measures on commutative Lie groups of infinite product type.
Ranked fragmentations
In this paper we define and study self-similar ranked fragmentations. We first show that any ranked fragmentation is the image of some partition-valued fragmentation, and that there is in fact a one-to-one correspondence between the laws of these two types of fragmentations. We then give an explicit construction of homogeneous ranked fragmentations in terms of Poisson point processes. Finally we use this construction and classical results on records of Poisson point processes to study the small-time...
Ranked Fragmentations
In this paper we define and study self-similar ranked fragmentations. We first show that any ranked fragmentation is the image of some partition-valued fragmentation, and that there is in fact a one-to-one correspondence between the laws of these two types of fragmentations. We then give an explicit construction of homogeneous ranked fragmentations in terms of Poisson point processes. Finally we use this construction and classical results on records of Poisson point processes to study the small-time behavior...
Regeneration in random combinatorial structures.
Regenerative partition structures.
Representation form of de Finetti theorem and application to convexity
Representation theorems for interacting Moran models, interacting Fisher-Wright diffusions and applications.
Restricted exchangeable partitions and embedding of associated hierarchies in continuum random trees
We introduce the notion of a restricted exchangeable partition of . We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In particular, we deduce from the general theory developed here a limit result conjectured previously for Ford’s alpha model and its extension, the alpha-gamma model, where restricted exchangeability arises naturally.
Self-similar fragmentations
Some consequences of the cyclic exchangeability property for exponential functionals of Lévy processes
Stochastic flows associated to coalescent processes II : stochastic differential equations