Julien Reygner CERMICS - ENPC 6 et 8 avenue Blaise Pascal Cité Descartes - Champs sur Marne 77455 MARNE LA VALLÉE E-mail : julien[.]reygner[@]enpc[.]fr (remove brackets, of course) My office: bâtiment Coriolis, B215 My phone: +33 1 64 15 35 72

Welcome!

I am an assistant professor at École des Ponts ParisTech, and a researcher within the Applied Probability team of CERMICS.

Teaching

• Office hours
• École des Ponts ParisTech:
  • 2A IMI/SEGF: Statistiques et analyse de données (page du cours sur Educnet).
  • 3A GMM, M2 DMSE: Ingénierie des incertitudes en mécanique (page du cours sur Educnet).
• Mines ParisTech:
  • 1A: Probabilités (page web du cours).
• Former courses

Research interests

• Long time behaviour of stochastic processes: convergence to equilibrium, metastability.
• Interacting particle systems and particle methods for nonlinear PDEs.
• Equilibrium and nonequilibrium statistical mechanics, large deviations, rare events.
• Applications of probability theory and analysis to physics, economics and operations research.
• Uncertainty quantification and industrial applications.

I am involved in the organisation of CERMICS' colloquium and applied mathematics seminar, and I regularly take part in the activities of the MSMath ERC project.

I am a member of the ANR project EFI (2017-2020).

PhD students

• Since 2017: Adrien Touboul, with Bernard Lapeyre at CERMICS and Pierre Benjamin, Fabien Mangeant and Mouadh Yagoubi at IRT SystemX.
• Since 2017: Mouad Ramil, with Tony Lelièvre at CERMICS.
• Since 2016: Sofiane Martel, with Sébastien Boyaval at LHSV.

Articles and preprints (HAL and arXiv versions may not be up to date)

• T. Lelièvre, L. Pillaud-Vivien, J. Reygner, Central Limit Theorem for stationary Fleming–Viot particle systems in finite spaces, ALEA Latin American Journal of Probability and Mathematical Statistics, 15:1163-1182, 2018 (arXiv:1806.04490).
• J. Reygner, Equilibrium large deviations for mean-field systems with translation invariance, Annals of Applied Probability, 28(5):2922-2965, 2018 (arXiv:1706.08780, complement).
• F. Bouchet, J. Reygner, Generalisation of the Eyring–Kramers transition rate formula to irreversible diffusion processes, Annales Henri Poincaré, 17(12):3499-3532, 2016 (arXiv:1507.02104).
• B. Jourdain, J. Reygner, Optimal convergence rate of the multitype sticky particle approximation of one-dimensional diagonal hyperbolic systems with monotonic initial data, Discrete and Continuous Dynamical Systems - Series A, 36(9):4963-4996, 2016 (arXiv:1507.01085).
• B. Jourdain, J. Reygner, A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data, Journal of Hyperbolic Differential Equations, 13(3):441-602, 2016 (arXiv:1501.01498).
• J. Reygner, Chaoticity of the stationary distribution of rank-based interacting diffusions, Electronic Communications in Probability 20(60):1-20, 2015 (arXiv:1408.4103).
• B. Jourdain, J. Reygner, Capital distribution and portfolio performance in the mean-field Atlas model, Annals of Finance 11(2):151-198, 2015 (arXiv:1312.5660).
• B. Jourdain, J. Reygner, The small noise limit of order-based diffusion processes, Electronic Journal of Probability 19(29):1-36, 2014 (arXiv:1307.0490).
• B. Jourdain, J. Reygner, Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation, Stochastic Partial Differential Equations: Analysis and Computations 1(3):455-506, 2013 (arXiv:1211.4818).
• A. Gaudillière, J. Reygner, Sampling the Fermi statistics and other conditional product measures, Annales de l'Institut Henri Poincaré : Probabilités et Statistiques 47(3):790-812, 2011 (arXiv:0911.4565).
• O. Durand de Gevigney, F. Meunier, C. Popa, J. Reygner, A. Romero, Solving coloring, minimum clique cover and kernel problems on arc intersection graphs of directed paths on a tree, 4OR - A Quarterly Journal of Operations Research 9(2):175-188, 2011 (arXiv:0902.1182).

Proceedings and survey articles

• J. Reygner, Long time behaviour and mean-field limit of Atlas models, ESAIM: Proceedings and Surveys (Journées MAS 2016 de la SMAI - Phénomènes complexes et hétérogènes), 60:132-143, 2017 (arXiv:1705.08140).
• J. Reygner, Merveilles du monde unidimensionnel : lois de conservation et transport optimal, MATAPLI 108:103-122, 2015.
• F. Bouguet, F. Malrieu, F. Panloup, C. Poquet, J. Reygner, Long time behavior of Markov processes and beyond, ESAIM: Proceedings and Surveys (Modélisation Aléatoire et Statistique - Journées MAS 2014), 51:193-211, 2015 (arXiv:1507.05801).

Vitae

During the academic year 2014-2015, I was a CNRS postdoctoral fellow at Laboratoire de Physique in ENS de Lyon, within the Climate and Statistical Mechanics group coordinated by Freddy Bouchet.

I defended my Ph.D. thesis at Université Pierre et Marie Curie in 2014 (see a short summary here). My advisors were Benjamin Jourdain and Lorenzo Zambotti.
This work was awarded the Prix de thèse Jacques Neveu 2014 by the group MAS of SMAI.

I am an Ingénieur des Ponts, des Eaux et des Forêts and a former undergraduate student of École Polytechnique.

My ORCID ID is 0000-0002-7005-0957, and my Google Scholar profile is here.

Souvenirs

• Meeting Uncertainty quantification in materials science, Institut Henri Poincaré, on 14 May 2018.
• SMAI-BOUM project Fluctuations dans les systèmes de particules, Institut Henri Poincaré, on 21-22 March 2016.
• Workshop Statistical mechanics and computations of large deviation rate functions in Centre Blaise Pascal at ENS de Lyon, on 16-19 June 2015.
• Groupe de travail Transport thermique at CERMICS and Inria Paris-Rocquencourt, from 2012 to 2014.
• Former talks