Page web de Raphaël Lachièze-Rey
raphael.lachieze-rey@math.cnrs.fr
I am "Maitre de conférences" (Assistant professor) in the Laboratoire MAP5 at the Université Paris Cité , in the probability team.
Member of the CNRS research group
GDR GEOSTO
Upcoming (or slightly passed :) events
- Workshop: Inhomogeneous random systems, , January 25 - 26 2023, Institut Curie and Institut Henri Poincaré, Paris
- Hyperuniform structures, rigid point processes and related topics, Feb 20 - 22, Lille
- workshop MESA on Stein's method, March 21 - 24 2023, Toulouse
- Unirandom conference on random nodal sets, June 3 - 9 2023, Rennes
Research interests
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Limit theorems in Stochastic Geometry
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Random sets, excursions and nodal sets
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Point processes, hyperuniformity and variance linearity
Team
Loïc Thomassey, PhD student, 2021 -
Diala Hawat, PhD student, 2020 -
Safa Ladgham,PhD student, 2018 - 2022, manuscrit
Works
my arXiv pagemy Hal page
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with Loïc Thomassey,
Nodal replication of random waves , 2023
[arXiv] -
with Safa Ladgham,
Local repulsion of planar Gaussian critical points , 2022
[arXiv] -
with Diala Hawat, Guillaume Gautier and Rémi Bardenet,
On estimating the structure factor of a point process, with applications to hyperuniformity
to appear in Statistics and Computing 2022
[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
to appear in Annales IHP B,
[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
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Mixing properties for STIT tessellations , 2011,
[arXiv]
Advances in Applied Probability Volume 43, Number 1 (2011), 40-48.
Theses
If you don't understand the CLT: Clic here
Processus de Poisson et applications (Master Mathématiques appliquées 2è année, Université de Paris)
Using Stein's method in random geometry ( Post-graduate course, University of Southern California, 2015)
- Lecture notes (several techniques using Stein's method to prove limit theorems for geometric functionals, with partial proofs)
Probabilités avancées (Master 1 MMA, Université de Paris)
Probabilités et statistiques (Licence Informatique è 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 2012-2013 (Licence Mathématiques 3é année, Université de Paris)
Integration 2012/2013 (Licence Mathématiques 3é année, Université de Paris)
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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.
Diffusion and popularization
- Intervention "Pint of Science"The dark spots of our Mathematical Intuition Vidéo
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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 .