Gaultier Lambert

My new email address is glambert at kth.se

About me

My mathematical interests lie at the interface between probability theory, analysis and mathematical physics. My research focuses on random matrices, statistical physics, and Gaussian Multiplicative Chaos. Here is a link to the webpage of the Random Matrices, Stochastic Models and Analysis at KTH.

Contact

glambert at kth.se
ORCID ID 0000-0001-5260-2239
Google scholar webpage

Dept. of Mathematics
KTH Royal Institute of Technology
Lindstedtsvägen 25, Stockholm

If you are interested in doing a PhD thesis in probability theory and mathematical physics and you would like to be working with me, I am actively looking for both PhD and Master students! So, please do not hesitate to contact me!,

Appointments

• 2023-: Associate Professor, Department of Mathematics, KTH Royal Institute of Technology.
• 2018-2022: Lecturer, Institut für Mathematik, University of Zurich.
• 2016-2018: Postdoc in the research group of Ashkan Nikeghbali, University of Zurich.
• 2016: PhD, Department of Mathematics, KTH Royal Institute of Technology under the supervision Kurt Johansson. Here you can find the manuscript of my thesis on "Fluctuations of smooth linear statistics of determinantal point processes".

Events

• Random Matrices and Scaling Limits 28 Aug.- 13 Dec. 2024, , Institute Mittag-Leffler, Stockholm (co-organizer).
• Research Workshop of The Israel Science Foundation, Random Matrices and Integrability in Complex and Quantum Systems, June 26-July 01 2024, Yad Hashmona.

Papers and preprints

1. Central limit theorem for smooth statistics of one-dimensional free fermions, with A. Deleporte.
2. Law of large numbers for the maximum of the two-dimensional Coulomb gas potential, with Thomas Leblé and O. Zeitouni.
3. Multiplicative chaos measures from thick points of log-correlated field, with J. Junnila and C. Webb.
4. From Berry-Esseen to super-exponential, with K. Courteaut and K. Johansson.
5. The characteristic polynomial of sums of random permutations and regular digraphs, with S. Coste and Y. Zhu
   International Mathematics Research Notices (2023).
6. Quantum statistics transmutation via magnetic flux attachment, with D. Lundholm and N. Rougerie
   Probability and Mathematical Physics (2023).
7. Universality for free fermions and the local Weyl law for semiclassical Schrödinger operators, with A. Deleporte
   Journal of the European Mathematical Society (2023).
8. Strong approximation of Gaussian β-ensemble characteristic polynomials: the edge regime and the stochastic Airy function, with E. Paquette.
9. Precise deviations for disk counting statistics of invariant determinantal processes, with M. Fenzl.
   International Mathematics Research Notices (2021).
10. Multivariate normal approximation for traces of random unitary matrices, with K. Johansson.
    Ann. Probab. 49, Number 6, 2961-3010 (2021).
11. Strong approximation of Gaussian β-ensemble characteristic polynomials: the hyperbolic regime, with E. Paquette.
    Ann. Appl. Probab. 33(1): 549-612 (2023)
12. Poisson statistics for Gibbs measures at high temperature.
    Ann. Inst. H. Poincaré Probab. Statist. 57(1), 326-350 (2021).
13. CLT for circular β-ensembles at high temperature, with A. Hardy.
    J. Funct. Anal. 280(7), Article 108869 (2021)
14. How much can the eigenvalues of a random Hermitian matrix fluctuate? with T. Claeys, B. Fahs and C. Webb.
    Duke Math. J. 170(9): 2085-2235 (2021)
15. Mesoscopic central limit theorem for the circular β-ensembles and applications.
    Electron. J. Probab. 26 (2021), paper no. 7.
16. Maximum of the characteristic polynomial of the Ginibre ensemble.
    Comm. Math. Phys. 378 (2020), no. 2, 943-985.
17. Quantitative normal approximation of linear statistics of β-ensembles, with M. Ledoux and C. Webb.
    Ann. Probab. 47, Number 5 (2019), 2619-2685
18. Incomplete determinantal processes: from random matrix to Poisson statistics.
    J. Stat. Phys. 176(6), 1343-1374 (2019)
19. Subcritical multiplicative chaos for regularized counting statistics from random matrix theory, with D. Ostrovsky and N. Simm.
    Commun. Math. Phys., Volume 360 (2018), Issue 1, 1-54
20. The law of large numbers for the maximum of almost Gaussian log-correlated random fields coming from random matrices, with E. Paquette.
    Probab. Theory Relat. Fields 173:157-209 (2019)
21. Limit theorems for biorthogonal ensembles and related combinatorial identities.
    Adv. Math. 329 (2018), 590-648
22. Mesoscopic fluctuations for unitary invariant ensembles
    Electron. J. Probab., Volume 23 (2018), paper no. 7, 33 pp
23. Gaussian and non-Gaussian fluctuations for mesoscopic linear statistics in determinantal processes, with K. Johansson.
    Ann. Probab. 46, Number 3 (2018), 1201-1278.
24. Symmetry-breaking phase transition in a dynamical decision model, with E. Bertin and G. Chevereau.
    J. Stat. Mech. P06005 (2011)

Research grants

• Swedish Foundations’ Starting Grant (Ragnar Söderbergs fellow)
• Göran Gustafsson prize for younger researchers (1,0 MSEK)
• VR (Swedish Research council) starting grant (4 MSEK) 2023-2026.
• Research participant for MSRI semester program Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Berkeley, fall 2021.
• Ambizione grant (S-71114-05-01, CHF 534364) from the Swiss National Science Foundation 2018-2022.
• UZH Forschungskredit grant (# FK-17-112, CHF 108639), 2017-2018.

Lectures

KTH

• Spring 2024: Time series analysis
• Spring 2023: Time series analysis

University of Zurich

• Fall 2020: Probability II, bachelor level course. Here you can download my lecture notes.
• Fall 2018: An introduction to Mathematical finance, bachelor level course.
• Spring 2018: Organization of a student seminar on Limit Theorems in Probability Theory
• Fall 2017: Lecturer for a bachelor and master level course on Markov Processes and Ergodic Theory
• Spring 2017: Lecturer for a master and graduate level course on Random Matrix Theory

Seminar talks

2023:

• Stockholm University (Nov. 15).
• Statistical properties of free fermions, SISSA, Trieste.
• Statistical properties of free fermions, ENS Lyon.
• Gaussian multiplicative chaos and random matrices, Lunds University.
• Universality for free fermions point processes, Analysis seminar, Beijing International Center for Mathematical Research, Peking University (online).

2022:

• Applications of the theory of Gaussian multiplicative chaos to random matrices, University of Michigan (online)
• Normal approximation for traces of random unitary matrices, IMPA (online)
• Approximations Gaussienne pour les statistiques de matrices aléatoires unitaires, Mini cours Séminaire MEGA, Institut Henri Poincaré, Paris
• Normal approximation for traces of random unitary matrices, University of California San Diego (online)

2021:

• Universality for free fermions point processes, One World mathematical physics seminar of the IAMP (video).
• Fluctuations of β-ensembles in the high temperature regime, Analysis and Probability seminar, TU Dresden (online).
• Normal approximation for traces of random unitary matrices, Rhein-Main Kolloquium Stochastik (online).
• The edge scaling limit of the characteristic polynomial of the Gaussian β-ensembles, Groupe de Travail de modélisation stochastique, Laboratoire de Probabilités, Statistique et Modélisation, Paris
• Applications of the theory of (subcritical) multiplicative chaos to random matrices, Séminaire MEGA, Institut Henri Poincaré, Paris (video)
• On the characteristic polynomial of the Gaussian β-ensemble, North British Probability seminars, University of Edinburgh (online)
• Applications of the theory of (subcritical) multiplicative chaos to random matrices, Korea Institute for Advanced Study (online)

2020:

• On the characteristic polynomial of the Gaussian β-ensemble, Seminar on Integrable Systems and Mathematical Physics at SISSA, Trieste (online)
• On the characteristic polynomial of the Gaussian β-ensemble, Probability Seminar, Durham University (online)
• What is... a random unitary matrix?, Zurich graduate colloquium
• Application of Stein's method to linear statistics of beta-ensembles, Random matrix theory seminar, Oxford University (online)
• Fluctuations of β-ensembles in the high temperature regime, Bielefeld-Melbourne Mathematical Physics seminar (online)
• Applications de la théorie du chaos multiplicatif Gaussien aux matrices aléatoires, Séminaire Probabilité et Statistique, Département de Mathématiques d'Orsay (online)

2019:

• Multivariate normal approximation for traces of random unitary matrices, Combinatorics Seminar, Ohio State University
• Multivariate normal approximation for traces of random unitary matrices, Columbia/Courant joint Probability seminar, New York
• How much can the eigenvalues of a random Hermitian matrix fluctuate?, Oberseminar Calculus of Variations and Applications, University of Munich (LUM)
• Applications of the theory of Gaussian multiplicative chaos to random matrices, Random Matrix Seminar, KTH Royal Institute of Technology
• Application de la méthode de Stein aux statistiques linéaires des β-ensembles, Séminaire Analyse, Université de Strasbourg

2018:

• How much can the eigenvalues of a random Hermitian matrix fluctuate? Seminar on stochastic processes, ETH Zürich
• How much can the eigenvalues of a random Hermitian matrix fluctuate? Seminar in Probability Theory, University of Basel
• Stein's method for normal approximation of linear statistics of beta-ensembles, Mathematical Physics Seminar at Geneva University
• Stein's method for normal approximation of linear statistics of beta-ensembles, Queen Mary University of London
• Gaussian Multiplicative Chaos and Random Matrices, Imperial College London

2017:

• Fluctuations of smooth eigenvalues statistics for unitary invariant ensembles of random matrices, University of Helsinki
• Fluctuations of smooth eigenvalues statistics for unitary invariant ensembles of random matrices, Alfréd Rényi Institute of Mathematics, Budapest
• Application de la méthode de Stein aux statistiques linéaires des beta-ensembles, Université de Lille
• Stein's method for normal approximation of linear statistics of beta-ensembles, KTH Royal Institute of Technology
• The Law of large numbers for the maximum of the log-characteristic polynomial of Unitary invariant ensembles, University of Bristol
• CLT for Beta ensembles with a rate of convergence in total-variation distance, Institut de Mathématiques de Toulouse

2016:

• Eigenvalues of Random Matrices and Multiplicative Chaos, University of Uppsala
• Fluctuations of eigenvalues of normal random matrices, University of Helsinki
• Fluctuations of linear statistics of determinantal processes, Geometric Functional Analysis and Probability Seminar, The Weizmann Institute of Science
• Fluctuations of linear statistics of determinantal processes, Horowitz Seminar on Probability, Ergodic Theory and Dynamical Systems, Tel Aviv University

2015:

• Fluctuations of linear statistics of determinantal processes, Stockholm-Uppsala Analysis and Probability Day
• Gaussian and non-Gaussian limit theorems for some determinantal systems of particles, KTH Royal Institute of Technology

Conferences and Workshops

• Workshop on Gaussian Multiplicative Chaos, Polish Academy of Sciences, Warsaw, June 2023.
  Talk: Gaussian multiplicative chaos and random matrices.
• High Dimensional Statistics and Random Matrices, Porquerolles, June 2023.
  Talk: Characteristic polynomial of the Gaussian beta ensemble.
• Coulomb gases and universality, Paris, Dec. 2022.
  Talk: Scaling limits of the Gaussian beta-ensemble characteristic polynomial.
• Random media and large deviations, a conference in honor of Ofer Zeitouni's 60th birthday. October 21-24, 2022, Courant Institute, New York.
• Random Matrices and Random Landscapes, Conference in honour of Yan Fyodorov's 60th birthday, July 2022.
  Talk: Universality for free fermions
• Random Matrices and Beyond, A conference in celebration of Kurt Johansson's 60th birthday. KTH, Stocxkholm, June 2022 (co-organizer).
• Determinantal and permanantal point processes, quantum physics and signal processing. ENS Lyon, June 2022.
  Mini course: Universality for free fermions
• Workshop Excursions in Integrability, SISSA, Trieste, May 2022.
  Talk: Universality for free fermions
• XVII Brunel–Bielefeld Workshop on Random Matrix Theory and Applications. , Dec. 2021.
  Talk: On quantum statistics transmutation and the Ginibre ensemble (online)
• Mini-Course: Introduction to fluctuations of β-ensembles, MSRI, Berkeley, Oct. 2021.
• Integrable structures in random matrix theory and beyond, MSRI workshop, Berkeley, Oct. 2021
  Talk: The edge scaling limit of the characteristic polynomial of the Gaussian β-ensembles
• Summer Workshop on Statistical Physics and Machine Learning, Les Houches, August 2020
  
• New Directions in Mathematics of Coulomb Gases and Quantum Hall Effect, Institute Mittag-Leffler, Stockholm, July 2019
  
• Summer school XI on Probability and Mathematical Physics in Ghiffa, Italy, Sep. 2018
  Mini-course on β-ensembles
• Workshop on Gaussian Fields in Random matrix theory , Institute Mittag-Leffler, Stockholm, June 2018
  Talk: Stein's method for normal approximation of linear statistics of beta-ensembles
• 40th conference on Stochastic Processes and their Application, Chalmers University of Technology, Gothenburg, June 2018
  Talk: Stein's method for normal approximation of linear statistics of beta-ensembles
• Research program at PCMI on Random Matrices, Park City, July 2017
• Critical phenomena for random matrices and integrable system, Université catholique de Louvain, June 2017
  Talk: The Law of large numbers for the maximum of the log-characteristic polynomial of unitary invariant ensembles.
• ProbabLY ON random matrices, ENS Lyon, April 2017
  Talk: Random matrices and Gaussian Multiplicative Chaos
• Random Matrices and Determinantal Process, CIRM Marseille, March 2017
• XII Brunel-Bielefeld Workshop, Brunel University London, December 2016
  Talk: Transition from random matrix to Poisson statistics
• Optimal and random point configurations: from statistical physics to approximation theory, Institut Henri Poincaré, Paris, June 2016
• Workshop on Random matrix theory and strongly correlated systems, University of Warwick, April 2016
• XI Brunel-Bielefeld Workshop, ZIF Bielefeld, December 2015
• Stochastic Processes and Random Matrices, Les Houches Summer School, July 2015
• Warsaw Summer School in Probability, University of Warsaw, June 2015
  Talk: Free fermions confined in a Gaussian potential
• Etats de la recherche en matrices aléatoires, Institut Henri Poincaré, Paris, December 2014
• Mathematics Meets Physics, on the occasion of Antti Kupiainen's 60th birthday, University of Helsinki, June 2014
• Workshop on Random matrices and Jacobi operators, Institut Mittag-Leffler, Stockholm, May 2014
• Summer school, Randomness in Physics and Mathematics, ZIF Bielefeld, August 2013
• Trondheim Spring School in Point Processes and Complex Analysis, NTNU, May 2013
• St Petersburg School in Probability and Statistical Physics, Chebyshev Laboratory at St. Petersburg State University, June 2012