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 (S711140501, 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 (# FK17112, 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.
If you are interested in doing a Master's thesis in probability theory related to any of the above topics and you would like to be working with me, I am actively looking for students! So, please do not hesitate to contact me!
Contact
gaultier.lambert@math.uzh.ch
Institut für Mathematik
Universität Zürich
Winterthurerstrasse 190, 8057 Zürich
Office: Campus Irchel Y27J06.
Papers and preprints
 Strong approximation of Gaussian βensemble characteristic polynomials: the edge regime and the stochastic Airy function, with
E. Paquette.

Precise deviations for disk counting statistics of invariant determinantal processes,
with M. Fenzl.
International Mathematics Research Notices. (2021)
 Multivariate normal approximation for traces of random unitary matrices, with
K. Johansson.
Ann. Probab. (2021+)
 Strong approximation of Gaussian βensemble characteristic
polynomials: the hyperbolic regime, with
E. Paquette.
 Poisson statistics for Gibbs measures at high temperature.
Ann. Inst. H. Poincaré Probab. Statist. 57(1), 326350, (2021)
 CLT for circular βensembles at high temperature, with
A. Hardy.
J. Funct. Anal. 280(7), Article 108869 (2021)
 How much can the eigenvalues of a random Hermitian matrix fluctuate? with
T. Claeys,
B. Fahs and
C. Webb.
Accepted by Duke Math. J. (2020+)
 Mesoscopic central limit theorem for the circular βensembles and applications.
Electron. J. Probab. 26 (2021), paper no. 7.
 Maximum of the characteristic polynomial of the Ginibre ensemble.
Comm. Math. Phys. 378 (2020), no. 2, 943985.
 Quantitative normal approximation of linear statistics of βensembles, with
M. Ledoux and
C. Webb.
Ann. Probab., Volume 47, Number 5 (2019), 26192685
 Incomplete determinantal processes: from random matrix to Poisson statistics.
J. Stat. Phys. 176(6), 13431374 (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, 154
 The law of large numbers for the maximum of almost Gaussian logcorrelated random fields coming from random matrices, with
E. Paquette.
Probab. Theory Relat. Fields 173:157209 (2019)
 Limit theorems for biorthogonal ensembles and related
combinatorial identities.
Adv. Math., Volume 329 (2018), 590648
 Mesoscopic fluctuations for unitary invariant ensembles
Electron. J. Probab., Volume 23 (2018), paper no. 7, 33 pp
 Gaussian and nonGaussian fluctuations for mesoscopic linear statistics in determinantal processes, with
K. Johansson.
Ann. Probab., Volume 46, Number 3 (2018), 12011278.
 Symmetrybreaking phase transition in a dynamical decision model, with
E. Bertin and G. Chevereau.
J. Stat. Mech. P06005 (2011)
My papers are all available on
arXiv.
Teaching
At the University of Zurich
At KTH Royal Institute of Technology
 20152016: Teaching assistant for Complex Analysis (SF1628) and Probability Theory (SF2940)
 20142015: Teaching assistant for Differential Equations and Transforms II (SF1629 ), Complex Analysis (SF1628) and Probability Theory (SF2940)
 20132014: Teaching assistant for Differential Equation I (SF1633) and Probability Theory (SF2940)
 20122013: Teaching assistant for Differential Equation I (SF1633) and Complex Analysis (SF1628)
Seminar talks
2021:
 Integrable structures in random matrix theory and beyond , MSRI, Berkeley,
10/1822
 Analysis and Probability seminar, TU Dresden
 RheinMain Kolloquium Stochastik, (online, June 11).
 Groupe de Travail de modélisation stochastique, Laboratoire de Probabilités, Statistique et Modélisation, Paris (online, May 27)
 Applications of the theory of (subcritical) multiplicative chaos to random matrices, Séminaire MEGA, Institut Henri Poincaré, Paris (online)
 On the characteristic polynomial of the Gaussian βensemble, 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 βensemble, Seminar on Integrable Systems and Mathematical Physics at SISSA, Trieste (online)
 On the characteristic polynomial of the Gaussian βensemble, Probability Seminar, Durham University (online)
 What is... a random unitary matrix?, Zurich graduate colloquium
 Application of Stein's method to linear statistics of betaensembles, Random matrix theory seminar, Oxford University (online)
 Fluctuations of βensembles in the high temperature regime, BielefeldMelbourne 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 βensembles, 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 betaensembles, Mathematical Physics Seminar at Geneva University
 Stein's method for normal approximation of linear statistics of betaensembles, 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 betaensembles, Université de Lille
 Stein's method for normal approximation of linear statistics of betaensembles, KTH Royal Institute of Technology
 The Law of large numbers for the maximum of the logcharacteristic polynomial of Unitary invariant ensembles, University of Bristol
 CLT for Beta ensembles with a rate of convergence in totalvariation 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, StockholmUppsala Analysis and Probability Day
 Gaussian and nonGaussian limit theorems for some determinantal systems of particles, KTH Royal Institute of Technology
Conferences and Workshops
 Summer Workshop on Statistical Physics and Machine Learning, Les Houches, August 2020
 New Directions in Mathematics of Coulomb Gases and Quantum Hall Effect, Institute MittagLeffler, Stockholm, July 2019
 Workshop on Brown measures and nonnormal ransom matrices, University of Toulouse, Nov. 2018
 Summer school XI on Probability and Mathematical Physics in Ghiffa, Italy, Sep. 2018
Minicourse on βensembles
 Workshop on Gaussian Fields in Random matrix theory , Institute MittagLeffler, Stockholm, June 2018
Talk: Stein's method for normal approximation of linear statistics of betaensembles
 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 betaensembles
 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 logcharacteristic 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 BrunelBielefeld 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 BrunelBielefeld 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 MittagLeffler, 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
Updated on December 21, 2020