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.

• Second version of my survey on hyperuniformity: [arXiv link] . It contains additions on finite volume hyperuniformity, construction of hyperuniform point processes, and numerical aspects.

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

My Hal page

My arXiv profile

• Hyperuniformity

  • R. Lachièze-Rey,
    From smooth to discontinuous kernels: a variance transfer principle for hyperuniform processes,
    Hal/arXiv, 2026

  • R. Lachièze-Rey,
    Maximal rigidity of random measure and uniqueness pairs: stealthy processes, quasicrystals and periodicity,
    to appear in J. Stat. Phys.,
    Hal/arXiv, 2025

  • R. Lachièze-Rey,
    Hyperuniform random measures, transport and rigidity (survey), to appear in the Series Stochastic Geometry, Modern research frontiers, Lecture notes in Mathematics, Springer
    Hal/arXiv, 2025

  • R. Lachièze-Rey,
    Rigidity of random stationary measures and applications to point processes,
    Hal/arXiv, 2024

  • R. Lachièze-Rey and Yogeshwaran D.,
    Hyperuniformity and optimal transport of point processes,
    Hal/arXiv, 2024

  • Diala Hawat, Rémi Bardenet and R. Lachièze-Rey,
    Repelled point processes with application to numerical integration,
    to appear in Scand. J. Stat.,
    Hal/arXiv, 2023
    [arXiv]

    Package Python MCRPPy
    

  • Diala Hawat, Guillaume Gautier, Rémi Bardenet and R. Lachièze-Rey
    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

  • R. Lachièze-Rey,
    Diophantine Gaussian excursions and random walks, 2022
    Electronic Journal of Probability, 27 (126), pp. 1–33
    [arXiv]

  Random fields excursions and zeros

  • C. Hirsch and R. Lachièze-Rey,
    Functional central limit theorem for topological functionals of Gaussian critical points,
    to appear in Ann. Appl. Prob.,
    Hal/arXiv, 2025

  • Loïc Thomassey and R. Lachièze-Rey,
    Nodal replication of random waves, 2023,
    to appear in Comm. Math. Phys.
    [arXiv]

  • R. Lachièze-Rey,
    Variance linearity for real Gaussian zeros, 2022
    Annales IHP, 58 (4), pp. 2114–2128
    [arXiv]

  • Safa Ladgham and R. Lachièze-Rey,
    Local repulsion of planar Gaussian critical points, 2023
    Stochastic Processes and their Applications, Vol. 166, 104221
    [arXiv]

  • R. Lachièze-Rey,
    Diophantine Gaussian excursions and random walks, 2022
    Electronic Journal of Probability, 27 (126), pp. 1–33
    [arXiv]

  • R. Lachièze-Rey and 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]

  • R. Lachièze-Rey and 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]

  • R. Lachièze-Rey,
    Bicovariograms and Euler characteristic of random fields excursions, 2019
    Stochastic Processes and their Applications, Volume 129, Issue 11, November 2019, Pages 4687–4703
    [arXiv]

  • R. Lachièze-Rey,
    Bicovariograms and Euler characteristic of regular sets, 2018
    Mathematische Nachrichten, 291 (2–3), pp. 398–419
    [arXiv]

  • R. Lachièze-Rey,
    An analogue of Kac–Rice formula for Euler characteristic, 2016
    [arXiv]

  • R. Lachièze-Rey,
    Concave majorant of stochastic processes and Burgers turbulence, 2012
    Journal of Theoretical Probability, June 2012, Volume 25, Issue 2, pp. 313–332
    [arXiv]

  • R. Lachièze-Rey and Youri Davydov,
    Rearrangements of Gaussian fields, 2011
    Stochastic Processes and their Applications, Volume 121, Issue 11, November 2011, Pages 2606–2628
    [arXiv]

  Inference on graphs

  • C. Hirsch, R. Lachièze-Rey and T. Owada,
    Normal approximation for subgraph counts in age-dependent random connection models, Hal/arXiv, 2025

  Applied spatial statistics

  • A. Erard, O. Cronie, R. Lachièze-Rey, R. Lorrillere,
    Land Sharing or Land Sparing? Implications for Farmland Birds of Conservation Concern in France, 2026, submitted

  • M. Mehdi Moradi, Ottmar Cronie, Ege Rubak, R. Lachièze-Rey, Jorge Mateu, Adrian Baddeley,
    Resample-smoothing of Voronoi intensity estimators, 2019
    Statistics and Computing, volume 29, pages 995–1010
    [arXiv]

  Limit theorems

  • R. Lachièze-Rey, Giovanni Peccati, Xiaochuan Yang,
    Quantitative two-scale stabilization on the Poisson space, 2022
    Annals of Applied Probability, 32 (4), 3085–3145
    [arXiv]

  • B. Arras, J. Breton, Aurélia Deshayes, Olivier Durieu, R. Lachièze-Rey,
    Some recent advances for limit theorems, 2019
    ESAIM: Proceedings and Surveys, 2020, Vol. 68, pp. 73–96

  • R. Lachièze-Rey,
    Normal convergence of nonlocalised geometric functionals and shot-noise excursions, 2019
    Annals of Applied Probability, Vol. 29, No. 5, 2613–2653
    [arXiv]

  • R. Lachièze-Rey, Matthias Schulte, Joe Yukich,
    Normal approximation for stabilizing functionals, 2019
    Annals of Applied Probability, Vol. 29 (2), pp. 931–993
    [arXiv]

  • Larry Goldstein, Tobias Johnson, R. Lachièze-Rey,
    Bounds to the normal for proximity region graphs, 2018
    Stochastic Processes and their Applications, Volume 128, Issue 4, April 2018, Pages 1208–1237
    [arXiv]

  • Andreas Basse-O'Connor, R. Lachièze-Rey, 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]

  • R. Lachièze-Rey, Giovanni Peccati,
    New Berry–Esseen bounds for functionals of binomial point processes, 2017
    Annals of Applied Probability, Volume 27, Number 4, 1992–2031
    [arXiv]

  • R. Lachièze-Rey, Sergio Vega,
    Boundary density and Voronoi set estimation for irregular sets, 2017
    Transactions of the AMS, 369, 4953–4976
    [arXiv]

  • R. Lachièze-Rey, 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]

  • R. Lachièze-Rey, 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]

  • R. Lachièze-Rey, 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

  • Bruno Galerne, R. Lachièze-Rey,
    Random measurable sets and covariogram realisability problems, 2015
    Advances in Applied Probability, Volume 47, Issue 3, September 2015, pp. 611–639
    [arXiv]

  • R. Lachièze-Rey, 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]

  • R. Lachièze-Rey,
    Realisability conditions for second order marginals of biphased media, 2015
    Random Structures and Algorithms, Volume 47, Issue 3, October 2015, Pages 588–604
    [arXiv]

  • R. Lachièze-Rey,
    The convex class of realisable unit covariances, 2013
    [arXiv]

  All works since 2015 (Hal)

Theses

• Habilitation thesis

• PhD thesis

Determinantal processes, random matrices and hyperuniformity (Université Paris Dauphine)

• Lecture notes

Introduction à la théorie de l'Information (Master Mathématiques appliquées 1è année, Université Paris Cité)

• Cours, exercices (m'écrire pour les corrigés)

Processus de Poisson et applications (Master Mathématiques appliquées 2è année, Université de Paris)

• Cours, exercices (m'écrire pour les corrigés)

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)

• Polycopié

Calcul differentiel (Licence Mathématiques 3é année, Université Paris Cité)

• Polycopié
• TDs

• Transfer principle for random matrix eigenvalues and Coulomb gases.

• Rigidity and maximal rigidity of random measures.

• Mini-course on Geometric functionals (Aarhus TDA summer school 2025).

• Mini-course on Hyperuniformity (Geosto 2025).

• Rigidity of point processes.

• Hyperuniformity exponent, rigidity and simulation.

• Functional CLT for Betti numbers of Gaussian excursions.

• Hyperuniformity and optimal transport of point processes.

• Replication d'ondes aléatoires

• Percolation d'excursions aléatoires -

• Ensembles nodaux gaussiens -

• Zéros des fonctions gaussiennes analytiques (présentation pour le GT Processus ponctuels répulsifs)

• Berry-Esseen bounds for geometric functionals

• Approximation d'ensembles (tres court)

• Berry-Esseen bounds for binomial functionals

• Voronoi approximation of irregular sets

• CLT for Poisson U-statistics: CLT for U-statistics in the Poisson chaos and applications to random graphs.

• TCL pour U-statistiques Poissoniennes: TCL pour U-statistiques géométriques dans le chaos poissonien.

• Realisability (eng, short version): Realisability problems with regularity conditions..

• Realisability (fr): Problemes de realisabilité avec conditions de regularité.

• Gaussian fields (fr): Réarrangements de champs gaussiens.

• Gaussian fields (eng): Rearrangements of Gaussian fields.

• PhD defense: Presentation, Université Lille 1.

• STIT tessellations (english): Ergodicity of STIT tessellations.

• STIT tessellations (francais): Ergodicité des mosaiques STIT.

Dissemination

• "Défisciences" lancé aux collégiens et lycéens paradoxe de Simpson
• 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]

• Visualisation interactive sur les illustres mathématiciens Français ou de tous les pays .