We define and study a family of Markov processes with state space the compact set of all partitions of N that we call exchangeable fragmentation-coalescence processes. They can be viewed as a… (More)

Coalescents with multiple collisions, also known as Λ-coalescents, were introduced by Pitman and Sagitov in 1999. These processes describe the evolution of particles that undergo stochastic… (More)

For a finite measure Λ on [0,1], the Λ-coalescent is a coalescent process such that, whenever there are b clusters, each k-tuple of clusters merges into one at rate ∫ 1 0 x(1− x)Λ(dx). It has… (More)

A branching process in random environment (Zn, n ∈ N) is a generalization of Galton Watson processes where at each generation the reproduction law is picked randomly. In this paper we give several… (More)

We develop an idea of Evans and O’Connell [13], Engländer and Pinsky [10] and Duquesne and Winkel [4] by giving a pathwise construction of the so called ‘backbone’ decomposition for supercritical… (More)

We describe a simple construction of Kingman’s coalescent in terms of a Brownian excursion. This construction is closely related to, and sheds some new light on, earlier work by Aldous (1998) and… (More)

Motivated by an evolutionary biology question, we study the following problem: we consider the hypercube {0, 1} where each node carries an independent random variable uniformly distributed on [0, 1],… (More)

We formulate the notion of the classical Fisher–Kolmogorov–Petrovskii– Piscounov (FKPP) reaction diffusion equation associated with a homogeneous conservative fragmentation process and study its… (More)

We describe a new general connection between Λ-coalescents and genealogies of continuousstate branching processes. This connection is based on the construction of an explicit coupling using a… (More)

Consider a graph in which each site is endowed with a value called fitness. A path in the graph is said to be “open” or “accessible” if the fitness values along that path is strictly increasing. We… (More)