Gaultier Lambert

My new email address is glambert at

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.


glambert at
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!,



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)
My papers are all available on arXiv.

Research grants



University of Zurich

Seminar talks










Conferences and Workshops

Updated on Oct. 15, 2023