About me CV
Since October 2023, I am associate professor (maître de conférence) at the engineer school Télécom SudParis, which is part of « Institut Polytechnique de Paris » and « Institut Mines-Télécom ».
I have been a postdoctoral researcher (2021-2023) at Ecole Polytechnique (CMAP) working with Sylvie Méléard and Vincent Bansaye. The subject of the postdoc consisted in studying the invasion phenomena in a population dynamics model. This question arises naturally, inter alia, in the study of the emergence of a cancer or an epidemy.
I have done my PhD thesis (2018-2021) at Université d’Evry (LaMME) under the supervision of Dasha Loukianova (Université d’Evry, LaMME) and Eva Löcherbach (Université Paris 1, SAMM). My thesis was dedicated to the study of large scale limit of (stochastic) particle systems in a diffusive regime, and particularly for systems with Hawkes-type dynamics. These particle systems are natural models for neural system and also for order books.
I am more generally interested in applications of mathematics and computer science to modelizations.
Research themes
- Stochastic analysis: stochastic differential equations (with jumps), (conditional) McKean-Vlasov equations, white noise, martingale problems, Markov processes, random environment, measure-valued processes, measure-variable functions
- Interacting particle systems: nonlinear Hawkes processes, birth-death processes, invasion models
- Large scale limits: mean field limits, (conditional) propagation of chaos, diffusive limits, population dynamics limits, quenched and annealed limits
Research
Preprints
- [12] V. Bansaye, N. Belmabrouk, X. Erny, S. Girel (2026+)
Invasion dynamics for a quasi-critical birth-death process.
Submitted (soon).
Links: HAL - [11] X. Erny (2025+)
The first Fundamental Theorem of Calculus for functions defined on Wasserstein space.
Submitted.
Links: ArXiv HAL
Published/Accepted Papers
- [10] X. Erny (2025)
Generators of measure-valued jump diffusions and convergence rate of diffusive mean-field models.
Electronic Journal of Probability 30: 1-44 (2025).
Links: EJP ArXiv HAL - [9] X. Erny (2025)
Annealed limit for a diffusive disordered mean-field model with random jumps.
Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 61(1): 510-532 (February 2025).
Links: AIHP ArXiv HAL - [8] V. Bansaye, X. Erny, S. Méléard (2024)
Sharp approximation and hitting times for stochastic invasion processes.
Stochastic Processes and their Applications 178 (December 2024), A tribute to Francis Comets
Links: SPA ArXiv HAL - [7] X. Erny, E. Löcherbach, D. Loukianova (2023)
Strong error bounds for the convergence to its mean field limit for systems of interacting neurons in a diffusive scaling.
Annals of Applied Probability 33(5): 3563-3586 (October 2023).
Links: AAP ArXiv HAL - [6] X. Erny (2022)
Mean field system of a two-layers neural model in a diffusive regime.
Mathematical Neuroscience and Applications, August 25, 2022, Volume 2.
Links: MNA ArXiv HAL - [5] X. Erny, E. Löcherbach, D. Loukianova (2022)
White-noise driven conditional McKean-Vlasov limits for systems of particles with simultaneous and random jumps.
Probability Theory and Related Fields 183, 1027-1073 (2022).
Links: PTRF ArXiv HAL - [4] X. Erny (2022)
Well-posedness and propagation of chaos for McKean-Vlasov equations with jumps and locally Lipschitz coefficients.
Stochastic Processes and their Applications, Volume 150, August 2022, 192-214.
Links: SPA ArXiv HAL - [3] X. Erny, E. Löcherbach, D. Loukianova (2022)
Mean field limits for interacting Hawkes processes in a diffusive regime.
Bernoulli 28 (1): 125-149 (February 2022).
Links: Bernoulli ArXiv HAL - [2] X. Erny (2021)
A convergence criterion for systems of point processes from the convergence of their stochastic intensities.
Electronic Communications in Probability 26 1-10 (2021).
Links: ECP ArXiv HAL - [1] X. Erny, E. Löcherbach, D. Loukianova (2021)
Conditional propagation of chaos for mean field systems of interacting neurons.
Electronic Journal of Probability 26 1-25 (2021).
Links: EJP ArXiv HAL
Conference (co-)organization
- Modèles Probabilistes et Statistiques pour la Biologie Université Paris Nanterre, 18-20 May 2026.
with Nadia Belmabrouk
Website - Statistical Inference for Particle Systems Insitut Henri Poincaré & Université d’Evry Paris-Saclay, 7-8 April 2026.
with Eva Löcherbach, Dasha Loukianova, Trâm Thi-Bao Ngô, Aurélien Velleret
Website
Talks
- Séminaire de Probabilités et Statistiques du LAGA Université Sorbonne Paris Nord, 17 March 2026.
Generators of measure-valued diffusions and convergence speed for mean field models - Séminaire de Probabilités ICJ/UMPA Université Lyon 1, 12 March 2026.
Generators of measure-valued diffusions and convergence speed for mean field models
Slides - Demi-journée CITI Télécom SudParis, SAMOVAR, 3 December 2025.
Convergence speed in law for particle systems
Slides - SPA Conference Contributed session « Propagation of chaos in life science models » 17 July 2025.
Conditional propagation of chaos for a neural model through the study of generators of measure-valued Markov processes.
Slides - Séminaire SOP Télécom SudParis, SAMOVAR, 16 May 2024.
Mean-field approximation for SDEs with jumps.
Slides - Groupe de travail PEIPS Ecole polytechnique, CMAP, 11 July 2023.
Approximations of invasion phases and invasion times for populations.
Slides - Summer School – Mean field model Henri Lebesgue Center, campus Beaulieu, Rennes, 12-16 June 2023.
Annealed limit and quenched control for a diffusive disordered mean-field model with random jumps.
Slides - Groupe de travail Mathématiques financières et actuarielles, probabilités numériques au LPSM 13 April 2023.
Conditional propagation of chaos for mean field particle systems.
Slides - Séminaire de Probabilités du MAP5 Université Paris Cité, 10 March 2023.
Annealed and quenched limits for a diffusive disordered mean-field model with random jumps.
Slides - Séminaire de Probabilités et Statistiques de l’université de Nice 31 January 2023.
Annealed limit for a diffusive disordered mean-field model with random jumps.
Slides - Séminaire de probabilités de l’IRMAR Université de Rennes, 4 April 2022.
Strong error bounds for the conditional propagation of chaos for mean field systems of neurons.
Slides - Séminaire du département DATA Université de Grenoble, LJK, 17 February 2022.
Strong error bounds for the conditional propagation of chaos for mean field systems of neurons.
Slides - Journées MAMOVI 14 December 2021.
Conditional propagation of chaos for mean field system of interacting neurons.
Slides - Journée d’accueil des post-doctorants franciliens 20 October 2021.
Particle system with random interaction.
Slides - International Conference in Mathematical NeuroScience 2021 online, 28 June 2021.
Conditional propagation of chaos for mean field system of neurons.
Slides Video - Séminaire SAMM Université Paris 1 Panthéon Sorbonne, 5 February 2021.
Conditional propagation of chaos for mean field systems of interacting neurons.
Slides - Séminaire PMF Université d’Evry, LaMME, 7 January 2021.
Conditional propagation of chaos for mean field systems of interacting neurons.
Slides - Groupe de travail PEIPS Ecole polytechnique, CMAP, 12 November 2020.
Conditional propagation of chaos for mean field systems of interacting neurons.
Slides - Journées des Probabilités 2019 Dourdan la Forêt, 24-28 June 2019.
Mean field limits for Hawkes processes in a diffusive regime.
Slides - Les Probabilités de Demain 2019 Université de Paris, campus des Grands Moulins, 14 June 2019.
Mean field limits for Hawkes processes in a diffusive regime.
Video
Poster
- International Conference on Mathematical Neuroscience 2020 online
Conditional propagation of chaos for mean field systems of interacting neurons.
Poster
Reports and thesis
- PhD thesis 2021 Université d’Evry
Large scale limits for interacting particle systems with simultaneous jumps in diffusive regime
Thesis - PhD thesis defence 30 June 2021 Université d’Evry
Slides - Master thesis 2018 Sorbonne Université
Limite de grande échelle de processus de Hawkes
Report - Internship report 2016 Ecole Normale Supérieure Paris-Saclay 2A
Modélisation thermodynamique des réseaux de régulation de gènes
Report - Internship report 2015 Ecole Normale Supérieure Paris-Saclay 1A
Les algorithmes de type Monte Carlo Tree Search appliqués aux Processus de Décisions Markoviens
Report
Teaching
Agrégation
Agrégation externe de Mathématiques option D (computer science), rank 97 (year 2017)
List (non-exhaustive) of « développements »: Développements
Current Teaching
- Télécom SudParis 2023-…
Old Teaching
- Télécom SudParis 2023-…
- 2023-2024 Teacher MAT8453, Probability and Statistics. 35h.
- 2023-2025 Teaching assistant MAT3101, Analysis and Integrals (1A Mathematics). 23h. Exercises
- Université Paris 1 Panthéon-Sorbonne 2022-2023
- 2022-2023 Teaching assistant, Statistics (L2 Mathematics). 30h.
- Ecole Polytechnique 2021-2023
- 2022-2023 Teaching assistant, Probability and Python projects, MAP361 (1A Mathematics). 22h. Exercises Projects
- 2021-2022 Teacher for the last session of the course « Mathematical modelling in neurosciences » of the master MSV. 3h. Course material
- Université d’Evry 2018-2021
- 2020-2021 Teaching assistant, Methodology (L1 Mathematics-Computer Science). 6h. Course material
- 2020-2021 Teaching assistant, Probability (L2 Physics). 18h. Exercises
- 2020-2021 Teaching assitant, Probability (L2 Mathematics). 39h. Exercises
- 2018-2020 Teaching assistant, Probability (L2 Mathematics/L2 Computer science). 39h. Exercises
- 2018-2020 Teaching assistant, Probability (L1 Biology). 15h. Exercises
- 2018-2020 Oral examiner, Algebra and Analysis (L1 Mathematics). 10h. Algebra exercises Analysis exercises
- Lycée Saint-Louis 2017-2018
- 2017-2018 Oral examiner, Mathematics (MPSI). Divers, Continuité, Dérivation, DL, Taylor, Intégration, Séries, Polynômes, Fractions rationnelles, EDO, Matrices, Espaces vectoriels, Déterminant, Espaces euclidiens
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