Page web de Raphaël Lachièze-Rey
raphael.lachieze-rey@math.cnrs.fr
Associate professor (HDR) at MAP5 (UPC) and INRIA Paris in the DYOGENE/MATHNET Team
Member of the CNRS research group
RT-MAIAGES
Upcoming (or slightly passed :) events
SPP-2265 Workshop on “Order and Disorder in Random Geometries: Hyperuniformity and Topological Data Analysis”, July 6–10, 2026, Castle of Reisensburg, Germany.
6th “SPP Workshop on Stochastic Geometry and Point Processes” on May 12, 2026, at the University of Paderborn, Germany
The 20th Anniversary of the Fourth Moment Theorem, December 11-12, 2025, MSA 3350, Belval Campus, University of Luxembourg
- Random Geometry, Graphs and extremes,27 - 31 October 2025 Dubrovnik, Croatia
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Mini course about Gaussian excursions and Topological Data Analysis at the 2025 TDA Danish summer school in Aarhus, Aug. 4-8 Download slides
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Mini-course abour Hyperuniformity at the 2025 GeoSto days in Grenoble, June 23-27
Survey
Download slides Organisation of the workshop Hyperuniformity and related topics , Dec. 11-13, Inria Paris
Intervention à la demi-journée consacrée aux distances de transport optimal, Nov. 29, 10am
Appariement optimal pour processus ponctuels stationnairesIntervention at the online OSSP seminar , Nov. 13 2024, 3pm
Hyperuniformity exponent: estimation, rigidity and simulation
Team
Giacomo Salvati, 2025 -
Rémi Bernard, 2025 -
Paul Rax, 2024 -
Adélie Erard, 2023 -
Loïc Thomassey, 2021 - 2025
Diala Hawat, 2020 - 2023
Safa Ladgham, 2018 - 2022
Works
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Hyperuniformity
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Maximal rigidity of random measure and uniqueness pairs: stealthy processes, quasicrystals and periodicity, Hal/arXiv, 2025
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Hyperuniform random measures, transport and rigidity, Hal/arXiv, 2025
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Rigidity of random stationary measures and applications to point processes, Hal/arXiv, 2024
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with Yogeshwaran D., Hyperuniformity and optimal transport of point processes, Hal/arXiv, 2024
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with Diala Hawat and Rémi Bardenet,
Package Python MCRPPy
Repelled point processes with application to numerical integration, Hal/arXiv, 2023
[arXiv]
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with Diala Hawat, Guillaume Gautier and Rémi Bardenet,
On estimating the structure factor of a point process, with applications to hyperuniformity, 2023
Statistics and Computing, volume 33, article number: 61
[arXiv]
Package Python : Structure factor, Approximate the structure factor of a stationary point process, test its hyperuniformity, and identify its class of hyperuniformity.
Lien GitHub -
Diophantine Gaussian excursions and random walks, 2022
Electronic Journal of Probability, 27 (126), pp. 1–33
[arXiv]
Inference on graphs
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with C. Hirsch, T. Owada, Normal approximation for subgraph counts in age-dependent random connection models, Hal/arXiv, 2025
Random fields excursions and zeros
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with C. Hirsch, Functional central limit theorem for topological functionals of Gaussian critical points, Hal/arXiv, 2025
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with Loïc Thomassey,
Nodal replication of random waves, 2023
[arXiv] -
Variance linearity for real Gaussian zeros, 2022
Annales IHP, 58 (4), pp. 2114–2128
[arXiv] -
with Safa Ladgham,
Local repulsion of planar Gaussian critical points, 2023
Stochastic Processes and their Applications, Vol. 166, 104221
[arXiv] -
Diophantine Gaussian excursions and random walks, 2022
Electronic Journal of Probability, 27 (126), pp. 1–33
[arXiv] -
with Stephen Muirhead,
Percolation of the excursion sets of planar symmetric shot noise fields, 2019
Stochastic Processes and their Applications, Volume 147, May 2022, Pages 175–209
[arXiv] -
with Stephen Muirhead,
Asymptotics for the critical level and a strong invariance principle for high intensity shot noise fields, 2021
Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, Vol. 59, No. 3, 1375–1397
[arXiv] -
Bicovariograms and Euler characteristic of random fields excursions, 2019
Stochastic Processes and their Applications, Volume 129, Issue 11, November 2019, Pages 4687–4703
[arXiv] -
Bicovariograms and Euler characteristic of regular sets, 2018
Mathematische Nachrichten, 291 (2–3), pp. 398–419
[arXiv] -
An analogue of Kac–Rice formula for Euler characteristic, 2016
[arXiv] -
Concave majorant of stochastic processes and Burgers turbulence, 2012
Journal of Theoretical Probability, June 2012, Volume 25, Issue 2, pp. 313–332
[arXiv] -
with Youri Davydov,
Rearrangements of Gaussian fields, 2011
Stochastic Processes and their Applications, Volume 121, Issue 11, November 2011, Pages 2606–2628
[arXiv]
Spatial statistics
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with M. Mehdi Moradi, Ottmar Cronie, Ege Rubak, Jorge Mateu, Adrian Baddeley,
Resample-smoothing of Voronoi intensity estimators, 2019
Statistics and Computing, volume 29, pages 995–1010
[arXiv]
Limit theorems
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with Giovanni Peccati, Xiaochuan Yang,
Quantitative two-scale stabilization on the Poisson space, 2022
Annals of Applied Probability, 32 (4), 3085–3145
[arXiv] -
with B. Arras, J. Breton, Aurélia Deshayes, Olivier Durieu,
Some recent advances for limit theorems, 2019
ESAIM: Proceedings and Surveys, 2020, Vol. 68, pp. 73–96 -
Normal convergence of nonlocalised geometric functionals and shot-noise excursions, 2019
Annals of Applied Probability, Vol. 29, No. 5, 2613–2653
[arXiv] -
with Matthias Schulte, Joe Yukich,
Normal approximation for stabilizing functionals, 2019
Annals of Applied Probability, Vol. 29 (2), pp. 931–993
[arXiv] -
with Larry Goldstein, Tobias Johnson,
Bounds to the normal for proximity region graphs, 2018
Stochastic Processes and their Applications, Volume 128, Issue 4, April 2018, Pages 1208–1237
[arXiv] -
with Andreas Basse-O'Connor and Mark Podolskij,
Power variation for a class of stationary increments Lévy driven moving averages, 2017
Annals of Probability, Vol. 45, No. 6B, 4477–4528
[arXiv] -
with Giovanni Peccati,
New Berry–Esseen bounds for functionals of binomial point processes, 2017
Annals of Applied Probability, Volume 27, Number 4, 1992–2031
[arXiv] -
with Sergio Vega,
Boundary density and Voronoi set estimation for irregular sets, 2017
Transactions of the AMS, 369, 4953–4976
[arXiv] -
with Matthias Reitzner,
U-statistics in stochastic geometry, 2016
Chapter in Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener–Itô Chaos Expansions and Stochastic Geometry, Springer, 2016
[arXiv] -
with Giovanni Peccati,
Fine Gaussian fluctuations on the Poisson space II: rescaled kernels, marked processes and geometric U-statistics, 2013
Stochastic Processes and their Applications, Volume 123, Issue 12, December 2013, Pages 4186–4218
[arXiv] -
with Giovanni Peccati,
Fine Gaussian fluctuations on the Poisson space I: contractions, cumulants and geometric random graphs, 2013
Electronic Journal of Probability, 18 (32), 1–32
Realisability
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with Bruno Galerne,
Random measurable sets and covariogram realisability problems, 2015
Advances in Applied Probability, Volume 47, Issue 3, September 2015, pp. 611–639
[arXiv] -
with Ilya Molchanov,
Regularity conditions in the realisability problem in applications to point processes and random closed sets, 2015
Annals of Applied Probability, Volume 25, Number 1 (2015), 116–149
[arXiv] -
Realisability conditions for second order marginals of biphased media, 2015
Random Structures and Algorithms, Volume 47, Issue 3, October 2015, Pages 588–604
[arXiv] -
The convex class of realisable unit covariances, 2013
[arXiv]
All works since 2015 (Hal)
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Theses
Determinantal processes, random matrices and hyperuniformity (Université Paris Dauphine)
Introduction à la théorie de l'Information (Master Mathématiques appliquées 1è année, Université Paris Cité)
Processus de Poisson et applications (Master Mathématiques appliquées 2è année, Université de Paris)
Chaines de Markov et applications
- Chaines de Markov et applications (pour les corrigés, écrire à raphael.lachieze-rey@parisdescartes.fr)
Numération
et logique (Licence Maths/info 1ère année, Université de Paris)
Calcul differentiel (Licence Mathématiques 3é année, Université Paris Cité)
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Mini-course on Geometric functionals (Aarhus TDA summer school 2025).
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Zéros des fonctions gaussiennes analytiques (présentation pour le GT Processus ponctuels répulsifs)
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CLT for Poisson U-statistics: CLT for U-statistics in the Poisson chaos and applications to random graphs.
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TCL pour U-statistiques Poissoniennes: TCL pour U-statistiques géométriques dans le chaos poissonien.
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Realisability (eng, short version): Realisability problems with regularity conditions..
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Realisability (fr): Problemes de realisabilité avec conditions de regularité.
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Gaussian fields (fr): Réarrangements de champs gaussiens.
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Gaussian fields (eng): Rearrangements of Gaussian fields.
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PhD defense: Presentation, Université Lille 1.
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STIT tessellations (english): Ergodicity of STIT tessellations.
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STIT tessellations (francais): Ergodicité des mosaiques STIT.
Dissemination
- Economie et sciences politiques: sensibilisation et analyse sur des données liées aux conflits d'interêt
- Intervention pour le workshop de l'ANR "Political Behaviors and Accountability" (Economix, Université de Nanterre) [Lien]
- Intervention au workshop Regards croisés sur la corruption et le favoritisme à Sciences Po, dans le cadre du Global Corruption Observatory.
- Auteur de l'article Qui sont les représentants d'intérêts? Une classification basée sur une analyse des données de la HATVP (lien pdf), publié dans la Revue Française d'Administration Publique.
- Outils de visualisation basés sur les données HATVP: [Lien] et [Lien].
- Vulgarisation sur statistiques et biais Timeworld 2021 au CNAM.
- Intervention: Quelles certitudes contient le hasard? [Programme] [Présentation] [Vidéo]
- Le simulateur en ligne: [Lien]
- Evènement Pint of Science 2022 sur le thème How our brain can mislead us [Programme] [Vidéo]
- Conférence pour la S.E.I.N: Comment le hasard agit-il sur nos vies? (2021) [Programme] [Vidéo]
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Visualisation interactive sur les illustres mathématiciens Français ou de tous les pays .