I'm a mathematician, interested in random and complex interacting systems.
Actually on leave at Qube Research and Technology (Paris).
My research interests lie principally in understanding large random interacting particle systems, including random matrix models, determinantal point processes, or Gibbs measures such as the Coulomb gas. More recently, I became interested in using such models for applications (numerical integration, machine learning & AI, signal processing, telecomunications, finance...).
Member of the INRIA team PARADYSE.
Member of the ANR JCJC BoB and the ERC StG BlackJack (PI: Rémi Bardenet).
See also [Google Scholar, MathSciNet, ArXiv]
CLT for circular beta-Ensembles at high temperature
with
Gaultier Lambert.
Preprint (2019)
[arXiv]
Mutual information of wireless channels and block-Jacobi ergodic operators
with Walid Hachem,
Shlomo Shamai.
IEEE Transactions on Information Theory (2019)
[arXiv, I3EIT]
DLR equations and rigidity for the Sine-beta process
with
David Dereudre,
Thomas Leblé,
Mylène Maïda.
Preprint (2018), to appear in Communications on Pure and Applied Mathematics
[arXiv]
Time-frequency transforms of white noises and Gaussian analytic functions
with
Rémi Bardenet.
Applied and Computational Harmonic Analysis (2019)
[arXiv,
ACHA]
Energy of the Coulomb gas on the sphere at low temperature
with
Carlos Beltrán.
Archive for Rational Mechanics and Analysis (2018)
[arXiv,
ARMA]
Polynomial ensembles and recurrence coefficients
Constructive Approximation (2018)
[arXiv,
CA]
Concentration for Coulomb gases and Coulomb transport inequalities
with
Djalil Chafaï,
Mylène Maïda.
Journal of Functional Analysis (2018)
[arXiv,
JFA]
Monte Carlo with determinantal point processes
with
Rémi Bardenet.
Annals of Applied Probability (2019)
[arXiv, AAP]
A survey on the eigenvalues local behavior of large complex correlated Wishart matrices
with
Walid Hachem, Jamal Najim.
ESAIM: Proceedings and surveys (2015)
[arXiv,
ESAIM]
Large complex correlated Wishart matrices: The Pearcey kernel and expansion at the hard edge
with
Walid Hachem, Jamal Najim.
Electronic Journal of Probability (2016)
[arXiv,
EJP]
Large complex correlated Wishart matrices: Fluctuations and asymptotic independence at the edges
with
Walid Hachem, Jamal Najim.
Annals of Probability (2016)
[arXiv,
AOP]
Average characteristic polynomials of determinantal point processes
Annales de l'Institut Henri Poincaré - Probabilités et Statistiques (2015)
[arXiv,
AIHP]
Large deviations for a non-centered Wishart matrix
with Arno
Kuijlaars.
Random Matrices: Theory and Applications (2013)
[arXiv,
RMTA]
A note on large deviations for 2D Coulomb gas with weakly confining potential
Electronic Communications in Probability (2012)
[arXiv,
ECP]
Weakly admissible vector equilibrium problems
with Arno
Kuijlaars.
Journal of Approximation Theory (2012)
[arXiv,
JAT]
Conference proceedings, other publications and notes:
A correspondence between zeros of time-frequency transforms and Gaussian analytic functions
with
Rémi Bardenet, Pierre Chainais, Julien Flamant.
13th International conference on sampling
theory and applications, SampTA 2019, Aug 2019, Bordeaux, France (2018) [HAL]
Processus ponctuels déterminantaux
with
Mylène Maïda.
Gazette des Mathématiciens (2018) [SMF]
An english version has also been published in the Newsletter of the EMS [EMS]
From random matrices to Monte Carlo integration via Gaussian quadrature
with Rémi Bardenet.
IEEE Statistical Signal processing workshop, 2018, Freiburg, Germany (2018) [HAL]
A note gathering some thoughts on the most used probability result in applications that is still confusing to me: the law of large numbers.
Courses (mainly in french):
(2019-2020) Concentration de la mesure et applications , M2 Recherche [Cours+TD]
(2019-2020) Chaînes de Markov et applications, M2 Ingénierie Statistique et Numérique [Cours+TP Python]
(2019-2020) Probabilités discrètes, L2 Math [TD]
(2018-2020) Probabilité, modèles et applications, M1 Ingénierie mathématique [Cours+TD]
(2017-2020) Séries temporelles, M1 Mathématiques pour la finance [Cours]
(2016-2020) Séries temporelles, M1 Mathématiques pour la finance [TP Python]
(2016-2018) Introduction to statistics, Ecole centrale de Lille, M1 Biomedical engineering[cours+TP R]
(2016-2018) Introduction aux processus ponctuels déterminantaux, M2 Recherche [Cours+TD]
(2015-2018) Traitement informatique de la statistique des données, M1 Ingénierie mathématique [cours+TP R et SAS]
(2015-2017) Mathématiques de base, L1 SVTE parcours aménagé [cours+TD]
(2015-2016) TD Mathématiques (analyse, algèbre, probabilités), Télécom Lille
PhD student: Mohamed Slim Kammoun (2017-), with Mylène Maïda.
Internship students: Imen Kerkeni (2018, Ecole Centrale Lille), Elvis Jourdant (2018, ENS Paris-Saclay).
Upcoming events (that I organize or particpate to)
The statistical physics of continuum particle systems with strong interactions (Singapore, January 2021)
Past events I organized
Determinantal point processes and fermions (Lille, February 2019)
Semaine d'Etude Math-Entreprise Hauts de France 2018 (Lille, February 2018)
1ère Journée Proba-Stat Lilloise (Lille, January 2017)
Journée de la fédération de recherche mathématique du Nord-Pas-de-Calais (Lille, October 2016)
Random matrices, free probability and determinantal processes (Lille, May 2016)
Since September 2020, I am on leave (en disponibilité) to work as a quantitative researcher at Qube Research and Technology (Paris).
Since September 2015, I am Maître de conférences (~Associate professor) in the Laboratoire Paul Painlevé, which is the mathematic department of the University of Lille.
During 2013-2015, I had a postdoctoral position at the Royal Institute of Technology (KTH) in the research team of Kurt Johansson.
In June 2013, I obtained a joint PhD degree (see the thesis) from KU Leuven, supervised by Arno Kuijlaars, and the Institut de Mathématiques de Toulouse, supervised by Michel Ledoux.
Before that, I studied in the Magistère de mathématiques de Strasbourg, including a Bachelor thesis with Janos Polonyi on quantum physics' axioms, a Magistère thesis with Jean-Bernard Zuber on quantum integrable systems (internship at the Laboratoire de Physique Théorique et Hautes Energies de Jussieu), and a Master thesis with Pierre van Moerbeke on random matrices and tillings (Erasmus exchange program with the Université Catholique de Louvain).
Scientific places I like to visit:
Libres pensées d'un mathématicien ordinaire (Djalil Chafaï's math Blog)
What's new (Terence Tao's math Blog)
Freakonometrics (Arthur Charpentier's math Blog)
Quanta Magazine (general science blog from the Simons Foundation)
Science étonnante (general science Youtube channel by David Louapre)
Heu?reka (economy & finance Youtube channel by Gilles Mitteau)
The mathematician's survival kit:
Digital Library of Mathematical Functions
The On-Line Encyclopedia of Integer Sequences
Math Overflow (research level math questions)
Math Stackexchange (student level math questions)
Email: adrien.hardy[you_know_what]univ-lille.fr