Clément Foucart

Maître de conférence à l'université Sorbonne Paris Nord (aka P13) au Laboratoire Analyse, Géométrie et Applications. En détachement à partir de septembre 2023 au CMAP (Ecole Polytechnique) au sein de l'ERC SINGER portée par Sylvie Méléard. My research focuses on some random processes often inspired by biological concepts such as "coalescent processes and branching processes."

Contact: foucart@math.univ-paris13.fr.

Aux étudiants d'un master 2 recherche en probabilités: vous pouvez me contacter si vous êtes intéressés pour faire un mémoire sur un des thémes suivants: processus de Lévy, processus de coalescence et ou fragmentation, processus de branchement.

Teaching/enseignement (2022)

Mini-course AMSS Summer School August 2022 : Continuous-state branching processes: genealogy, duality, interaction. Summary. Slides Talks 1 and 2 (genealogy) Slides Talk 3 (interaction).

Master M2 Probabilités et Applications et Master Math Fonda: Processus de branchement en temps et espace continus: Résumé du cours, Rappels Processus de Markov

Sujet de l'examen et Eléments de correction

Master M1 MEEF Probabilités et Statistiques pour le Master Enseignement: polycopié de cours, polycopié d'exercices (partie discrète) polycopié d'exercices (partie continue)

Remise à niveau Maths pour l'Ingénieur, SupGalilée: notes manuscrites de cours

Preprints/Prépublications (do not hesitate to contact me for latest/published versions.)

Behaviors near explosion of nonlinear CSBPs with regularly varying mechanisms, with Bo Li and Xiaowen Zhou, ArXiv

Weak convergence of continuous-state branching processes with large immigration, with Linglong Yuan ArXiv

Local explosions and extinction in continuous-state branching processes with logistic competition ArXiv

Publications

Extremal shot noise processes and random cutout sets, with Linglong Yuan (to appear in Bernoulli) ArXiv

Continuous-state branching processes with collisions: first passage times and duality, with Matija Vidmar (Stochastic Processes and their Applications, 2023) Journal, ArXiv

On the boundary classification of $\Lambda$-Wright-Fisher processes with frequency-dependent selection, with Xiaowen Zhou (Annales Henri Lebesgue, Volume 6 (2023), pp. 493-539.) Journal

Asymptotic behaviour of ancestral lineages in subcritical continuous-state branching populations, with Martin Moehle (Stochastic Process. Appl. 150, 510–531 (2022)) Journal

Limit theorems for continuous-state branching processes with immigration, with Chunhua Ma and Linglong Yuan (Advances in Applied Probability 54.2 (June 2022).) ArXiv

On the explosion of the number of fragments in the simple exchangeable fragmentation-coalescence processes, with Xiaowen Zhou (Ann. Inst. Henri Poincaré Probab. Stat. 2022, Vol. 58, No. 2, 1182–1207) Article

A phase transition in the coming down from infinity of simple exchangeable fragmentation-coagulation processes (Annals of Applied Probability 2022, Vol. 32, No. 1, 632-664.) Article, Journal

Time-changed spectrally positive Lévy processes started from infinity, with Pei-Sen Li and Xiaowen Zhou (Bernoulli 2021, Vol. 27, No. 2, 1291-1318.) ArXiv, Journal

On the entrance at infinity of Feller processes with no negative jumps, with Pei-Sen Li and Xiaowen Zhou (Statistics and Probability Letters (2020)) ArXiv, Journal

Coalescences in Continuous-State Branching Processes, with Chunhua Ma and Bastien Mallein, (Electron. J. Probab. 24, (2019), no. 103) Journal

Continuous-state branching processes with competition: duality and reflection at infinity, (Electron. J. Probab. 24 (2019), no. 33) Journal

Continuous-state branching processes, extremal processes and super-individuals with Chunhua Ma ( Ann. Inst. Henri Poincaré Probab. Stat. 55 (2019), no. 2). ArXiv (final version)

On the hitting times of continuous-state branching processes with immigration with Xan Duhalde and Chunhua Ma, (Stochastic processes and their Applications Vol. 124, Issue 12, (2014).

The impact of selection in the Lambda-Wright-Fisher model. (Electronic Communication of Probability, no 72, Vol.18, (2013)).

Local extinction in continuous-state branching processes with immigration with Gerónimo Uribe Bravo, Bernoulli Volume 20, Number 4 (2014)

Stable continuous-state branching processes with immigration and Beta-Fleming-Viot processes with immigration, with Olivier Hénard. Electronic Journal of Probability, Vol.18, (2013), no.23, 1-21.

Generalized Fleming-Viot processes with immigration via stochastic flows of partitions. ALEA, Lat. Am. J. Probab. Math. Stat. 9(2), 451-472 (2012)

Distinguished exchangeable coalescents and generalized Fleming-Viot processes with immigration. Advances in Applied Probability, June 2011, Vol.43 no 2