About Me
I am a postdoctoral reasearcher at INRAE Montpellier, working at the UMR Mistea with Bertrand Cloez where we work on the study of the fluctuations of supercritical 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 dynamic 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 or SIR models. Previously, I obtained my PhD degree at Université de Lorraine and INRIA Grand Est, working at Institut Elie Cartan de Lorraine in Nancy, under the supervision of Coralie Fritsch and Denis Villemonais. During my PhD thesis I worked on the study of bisexual Galton-Watson branching processes.
Recent Publications
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.
The Multi-type bisexual Galton-Watson branching process, with Coralie Fritsch and Denis Villemonais.
Abstract: In this work we study the bisexual Galton-Watson process with a finite number of types, where females and males mate according to a “mating function” and form couples of different types. We assume that this function is superadditive, which in simple words implies that two groups of females and males will form a larger number of couples together rather than separate. Leveraging on concave Perron-Frobenius theory, we prove a necessary and sufficient condition for almost sure extinction as well as a law of large numbers. Finally, we study the almost sure long-time convergence of the rescaled process through the identification of a supermartin- gale, and we give sufficient conditions to ensure a convergence in L1 to a non-degenerate limit.
Restricted maximum of non-intersecting Brownian bridges, with Yamit Yalanda
Abstract: Consider a system of N non-intersecting Brownian bridges in [0,1], and let M_N(p) be the maximal height attained by the top path in the interval [0, p], p ∈ [0, 1]. It is known that, under a suitable rescaling, the distribution of M_N(p) converges, as N → ∞, to a one-parameter family of distributions interpolating between the Tracy-Widom distributions for the Gaussian Orthogonal and Unitary Ensembles (corresponding, respectively, to p → 1 and p → 0). It is also known that, for fixed N , M_N(1) is distributed as the top eigenvalue of a random matrix drawn from the Laguerre Orthogonal Ensemble. Here we show a version of these results for M_N(p) for fixed N , showing that M_N(p)/√p converges in distribution, as p → 0, to the righmost charge in a generalized Laguerre Unitary Ensemble, which coincides with the top eigenvalue of a random matrix drawn from the Antisymmetric Gaussian Ensemble.