Photo

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.

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

  1. Strong approximation of Gaussian β-ensemble characteristic polynomials: the edge regime and the stochastic Airy function, with E. Paquette.
  2. Precise deviations for disk counting statistics of invariant determinantal processes, with M. Fenzl.
  3. Multivariate normal approximation for traces of random unitary matrices, with K. Johansson.
  4. Strong approximation of Gaussian β-ensemble characteristic polynomials: the hyperbolic regime, with E. Paquette.
  5. Poisson statistics for Gibbs measures at high temperature.
    Accepted by Ann. Inst. H. Poincaré Probab. Statist. (2020+)
  6. CLT for circular β-ensembles at high temperature, with A. Hardy.
    Accepted by J. Functional Analysis (2020+)
  7. How much can the eigenvalues of a random Hermitian matrix fluctuate? with T. Claeys, B. Fahs and C. Webb.
  8. Mesoscopic central limit theorem for the circular β-ensembles and applications.
  9. The law of large numbers for the maximum of the characteristic polynomial of the Ginibre ensemble.
    Comm. Math. Phys. 378 (2020), no. 2, 943-985.
  10. Quantitative normal approximation of linear statistics of β-ensembles, with M. Ledoux and C. Webb.
    Ann. Probab., Volume 47, Number 5 (2019), 2619-2685
  11. Incomplete determinantal processes: from random matrix to Poisson statistics.
    J. Stat. Phys. 176(6), 1343-1374 (2019)
  12. 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
  13. 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)
  14. Limit theorems for biorthogonal ensembles and related combinatorial identities.
    Adv. Math., Volume 329 (2018), 590-648
  15. Mesoscopic fluctuations for unitary invariant ensembles
    Electron. J. Probab., Volume 23 (2018), paper no. 7, 33 pp
  16. Gaussian and non-Gaussian fluctuations for mesoscopic linear statistics in determinantal processes, with K. Johansson.
    Ann. Probab., Volume 46, Number 3 (2018), 1201-1278.
  17. Symmetry-breaking 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

Seminar talks

2020:

2019:

2018:

2017:

2016:

2015:

Conferences and Workshops

Updated on September 15, 2020