Gaultier Lambert
About me
I am a research fellow at the Institut für Mathematik at the University of Zurich,
My research is supported by an ambizione grant (S-71114-05-01, CHF 534364) from the Swiss National Science Foundation.
I did my Ph.D. under the supervision of Kurt Johansson at KTH Royal Institute of Technology in Stockholm.
Here you can find the manuscript of my thesis on
"Fluctuations of smooth linear statistics of determinantal point processes" that I defended in June 2016. From September 2016 to December 2018, I was a postdoc at the University of Zurich in the research group of Ashkan Nikeghbali. In 2017, I received a grant from the UZH Forschungskredit (# FK-17-112, CHF 108639) to support my research.
My mathematical interests lie at the interface between probability theory, analysis, combinatorics and mathematical physics. My research focuses on random matrices, statistical physics, and Gaussian Multiplicative Chaos.
Contact
gaultier.lambert@math.uzh.ch
Institut für Mathematik
Universität Zürich
Winterthurerstrasse 190, 8057 Zürich
Office: Campus Irchel Y27J06.
Papers and preprints
- CLT for Circular beta-Ensembles at High Temperature, with A. Hardy.
- How much can the eigenvalues of a random Hermitian matrix fluctuate? with T. Claeys, B. Fahs and C. Webb
- Mesoscopic central limit theorem for the circular β-ensembles and applications.
- The law of large numbers for the maximum of the characteristic polynomial of the Ginibre ensemble.
- Quantitative normal approximation of linear statistics of β-ensembles, with M. Ledoux and C. Webb.
Ann. Probab. (2019+)
- Incomplete determinantal processes: from random matrix to Poisson statistics.
J. Stat. Phys. (2019)
- 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
- 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)
- Limit theorems for biorthogonal ensembles and related
combinatorial identities.
Adv. Math., Volume 329 (2018), 590-648
- Mesoscopic fluctuations for unitary invariant ensembles
Electron. J. Probab., Volume 23 (2018), paper no. 7, 33 pp
- Gaussian and non-Gaussian fluctuations for mesoscopic linear statistics in determinantal processes, with K. Johansson.
Ann. Probab., Volume 46, Number 3 (2018), 1201-1278.
- Symmetry-breaking phase transition in a dynamical decision model, with E. Bertin and G. Chevereau.
J. Stat. Mech. P06005 (2011)
My papers are also available on arXiv
Teaching
At the University of Zurich
At KTH Royal Institute of Technology
- 2015-2016: Teaching assistant for Complex Analysis (SF1628) and Probability Theory (SF2940)
- 2014-2015: Teaching assistant for Differential Equations and Transforms II (SF1629 ), Complex Analysis (SF1628) and Probability Theory (SF2940)
- 2013-2014: Teaching assistant for Differential Equation I (SF1633) and Probability Theory (SF2940)
- 2012-2013: Teaching assistant for Differential Equation I (SF1633) and Complex Analysis (SF1628)
Conferences and Workshops
- New Directions in Mathematics of Coulomb Gases and Quantum Hall Effect, Institute Mittag-Leffler, Stockholm, July 2019
- Workshop on Brown measures and non-normal ransom matrices, University of Toulouse, Nov. 2018
- 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
- 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
Seminar talks
2019:
- 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
Updated on September 3, 2019