Nicolas Fournier

A microscopic probabilistic description of a locally regulated population and macroscopic approximations

We consider a discrete model describing a locally regulated spatial population with mortality selection. This model was studied in parallel by Bolker and Pacala, [2] and Dieckmann, Law and Murrell [9], [4], [10]. We first generalize this model by adding spatial dependence. Then we give a path-wise description in terms of Poisson point measures. We show that different re-normalizations may lead to different macroscopic approximations of this model. The first approximation is deterministic and gives a rigorous sense to the number density. The second one is a superprocess already studied by Etheridge [6]. Finally, we study in specific cases the long time behavior of the system and of its deterministic approximation.

On the rate of convergence in Wasserstein distance of the empirical measure

Let

Propagation of chaos for the 2D viscous vortex model

\mu _N

A PURE JUMP MARKOV PROCESS WITH A RANDOM SINGULARITY SPECTRUM

μN be the empirical measure associated to a

On the Uniqueness for the Spatially Homogeneous Boltzmann Equation with a Strong Angular Singularity

N

HAWKES PROCESSES ON LARGE NETWORKS

N-sample of a given probability distribution