Xavier Erny's homepage

Xavier Erny

Email: xavier.erny@telecom-sudparis.eu

Orcid: https://orcid.org/0000-0002-3960-4085

Google scholar

About me CV

Since October 2023, I am assistant 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

  • [10] X. Erny (2024+)
    Study of measure-valued Markov processes. Explicit bounds for the convergence in distribution of mean-field models.
    Submitted.
    Links: ArXiv HAL
  • [9] V. Bansaye, X. Erny, S. Méléard (2022+)
    Sharp approximation and hitting times for stochastic invasion processes.
    In revisions at Stochastic Processes and their Applications, special issue « A Tribute to Francis Comets ».
    Links: ArXiv HAL

Published Papers

  • [8] X. Erny (2022+)
    Annealed limit for a diffusive disordered mean-field model with random jumps.
    Accepted at Annales de l’Institut Henri Poincaré, Probabilités et Statistiques.
    Links: 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

Talks

  • 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

  • Telecom SudParis 2023-…
    • 2023-… Teacher MAT8453, Probability and Statistics. 35h. Course material
    • 2023-… Teaching assistant MAT3101, Analysis and Integrals (1A Mathematics). 23h. Exercises
    • 2023-… Teaching assistant MAT4513, Numerical simulations and Extremal values (2A Mathematics)

Old Teaching













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