Researcher at INRIA Paris in the DYOGENE Team / Laboratoire MAP5 at the Université Paris Cité .

Member of the CNRS research group GDR GEOSTO

Research interests

• Point processes, hyperuniformity and rigidity

• Limit theorems in Stochastic Geometry

• Random fields, excursions and nodal sets

Team

• Adélie Erard, PhD student, 2023 -

• Loïc Thomassey, PhD student, 2021 -

• Diala Hawat, PhD student, 2020 -

• Safa Ladgham,PhD student, 2018 - 2022, manuscrit

Works

• with Yogeshwaran D.,
  Hyperuniformity and optimal transport of point processes 2024
  
  

• with Diala Hawat and Rémi Bardenet,
  Repelled point processes with application to numerical integration 2023
  [arXiv]
  

• with Loïc Thomassey,
  Nodal replication of random waves , 2023
  [arXiv]

• with Safa Ladgham,
  Local repulsion of planar Gaussian critical points , 2023
  to appear in Stochastic Processes and their Applications
  [arXiv]

• 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]
  Production d'un Package Python, Structure factor, An open-source Python package for studying the hyperuniformity of a spatial point process via the estimation of its structure factor.
  Lien Github

• 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]

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

• with Giovanni Peccati, Xiaochuan Yang
  Quantitative two-scale stabilization on the Poisson space, 2020
  Annals of Applied Probability, 32 (4), 3085-3145
  [arXiv]

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

• with Stephen Muirhead
  Percolation Of The Excursion Sets Of Planar Symmetric Shot Noise Fields, 2019
  [arXiv] Stochastic Processes and their Applications,Volume 147, May 2022, Pages 175-209

• with B. Arras, J. Breton, Aurelia Deshayes, Olivier Durieu
  SOME RECENT ADVANCES FOR LIMIT THEOREMS, 2019
  ESAIM: PROCEEDINGS AND SURVEYS, 2020, Vol. 68, p. 73-96

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

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

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

• Bicovariograms and Euler characteristic of random fields excursions, 2019,
  [arXiv]
  Stochastic Processes and their applications, Volume 129, Issue 11, November 2019, Pages 4687-4703

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

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

• with Andreas Basse-O'Connor and Mark Podolskij,
  Power variation for a class of stationary increments Lévy driven moving averages, 2017 ,
  [arXiv],
  Annals of Probability 2017, Vol. 45, No. 6B, 4477-4528.

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

• with Sergio Vega,
  Boundary density and Voronoi set estimation for irregular sets , 2017,
  [Arxiv]
  Transactions of the AMS 369, 2017, 4953-4976 ,

• An analogue of Kac-Rice formula for Euler characteristic, 2016,
  [arXiv]

• with Matthias Reitzner,
  U-statistics in stochastic geometry , 2016
  [arXiv],
  chapter in "Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Ito chaos expansions and stochastic geometry", 2016, Springer.

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

• with Ilya Molchanov,
  Regularity conditions in the realisability problem in applications to point processes and random closed sets , 2015,
  [arXiv]
  Annals of Applied Probability , Volume 25, Number 1 (2015), 116-149.

• Realisability conditions for second order marginals of biphased media , 2015,
  [arXiv]
  Random Structures and Algorithms,Volume47, Issue3 October 2015 , Pages 588-604.

• with Giovanni Peccati,
  Fine Gaussian fluctuations on the Poisson space II: rescaled kernels, marked processes and geometric U -statistics , 2013,
  [arXiv]
  Stochastic Processes and their applications, Volume 123, Issue 12, December 2013, Pages 4186-4218,

• with Giovanni Peccati,
  Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphss , 2013,
  Electronic Journal of Probability 18 (2013), no. 32, 1–32. 2013.

• The convex class of realisable unit covariances , 2013,
  [arXiv]

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

• with Youri Davydov,
  Rearrangements of Gaussian fields , 2011,
  [arXiv]
  Stochastic processes and their applications,Volume 121, Issue 11, November 2011, Pages 2606-2628
  

• Mixing properties for STIT tessellations , 2011,
  [arXiv]
  Advances in Applied Probability Volume 43, Number 1 (2011), 40-48.
  

Theses

• Habilitation thesis

• PhD thesis

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

• 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.

Diffusion and popularization

• Intervention "Pint of Science"The dark spots of our Mathematical Intuition Vidéo

• Conférence pour TimeWorld 2021Quelles certitudes contient le hasard? (Centre National des Arts et Métiers): Vidéo Slides ici

  Simulation de propagation de rumeur dans un réseau social

• Conférence pour la S.E.I.N:> Hasard, mesure et perception (avril 2021)
  Vidéo
  Slides SEIN

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