About Me
I am a postdoctoral reasearcher at INRAE Montpellier, working at the UMR Mistea with Bertrand Cloez studying the fluctuations of supercritical infinite-dimensional branching processes. My research focuses mainly in the interface of probability theory and population dynamics. My main interest is the study of processes describing the evolution of populations that can be affected by stochastic factors such as reproduction, mating, mutations or infections, and how these factors influence their asymptotic behavior both in long time and/or in large initial population settings. In particular, I am intereseted in models such as branching processes, individual-based models and growth-fragmentation processes. Previously, I obtained my PhD degree at Université de Lorraine and INRIA Grand Est, under the supervision of Coralie Fritsch and Denis Villemonais, where I worked on the study of bisexual Galton-Watson branching processes. My PhD manuscript can be found here.
Recent Publications
On ecological models with sublinear growth with Nicolas Champagnat, Pablo Marquet, Cristóbal Quiñinao, Rolando Rebolledo, Mauricio Tejo and Leonardo Videla
Abstract: Deterministic sublinear growth models have been used recently to enlighten the diversity-stability debate. Some values of the parameter θ, quantifying the super- or sub-linearity of births or deaths in the model, lead to unbounded individual birth rates for small densities, which suggests that the path to extinction in these models might make them biologically unrealistic and hence unsuitable to model ecological dynamics. In this work, we examine stochastic birth-death and diffusion versions of these models, for which we fully characterize the extinction properties. Our analysis leads us to conclude that sublinear models show some mathematical appeal but should be taken with caution when modeling biological phenomena, since they give rise to stochastic dynamics that either never go extinct, even for small initial populations, or go extinct almost surely, but on unrealistically long time scales.
Central limit theorems for branching processes under mild assumptions on the mean semigroup, with Bertrand Cloez
Abstract: We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment assumption and the exponential convergence of the mean semigroup in a weighted total variation norm. This latter assumption is pretty weak and does not necessitate symmetric properties or specific spectral knowledge on this semigroup. In particular, we recover two of the three known regimes (namely the small and critical branching processes) of convergence in known cases, and extend them to a wider family of processes. To prove our central limit theorems, we use the Stein's method, which in addition allows us to newly provide a rate of convergence to this type of convergence.
Quasi-limiting behaviour of the sub-critical multitype bisexual Galton-Watson branching process, with Coralie Fritsch and Denis Villemonais
Abstract: We investigate the quasi-limiting behaviour of bisexual subcritical Galton-Watson branching processes. While classical subcritical Galton-Watson processes have been extensively analyzed, bisexual Galton-Watson branching processes present unique difficulties because of the lack of the branching property. To prove the existence of and convergence to one or several quasi-stationary distributions, we leverage on recent developments linking bisexual Galton-Watson branching processes extinction to the eigenvalue of a concave operator.