My research lies for the most part in probability theory, especially in the study of integrable models of non-Hermitian random matrices, their eigenvector statistics, and their spectral stability under perturbations.
I am also interested in topics such as random permutations, combinatorics, and in applications of probability theory to other fields.
Publications and preprints
- G. Dubach, A. Fares, L. Thomas. On stability of outliers from the circular law. Preprint, arXiv:2606.16609 (2026).
- G. Dubach, H.A. Mai. On a random matrix proof of a bipartite Harer–Zagier formula. Preprint, arXiv:2606.05430 (2026).
- G. Dubach. Du bon usage des filtres. Revue de la filière mathématique (RMS) 137-1 (2026). In French.
- L. Benigni, S. Coste, G. Dubach. The delocalization of eigenvectors of real elliptic matrices. Preprint, arXiv:2602.10264 (2026).
- P. Bourgade, G. Dubach, L. Hartung, A. Keles. Fisher–Hartwig asymptotics for non-Hermitian random matrices. Preprint, arXiv:2512.09123 (2025).
- P. Deift, G. Dubach, C. Tomei, T. Trogdon. The Toda Lattice and Universality for the Computation of the Eigenvalues of a Random Matrix. London Mathematical Society Lecture Note Series 500, Cambridge University Press (2025).
- G. Dubach, J. Reker. Une brève histoire des perturbations non hermitiennes de rang un. Gazette de la Société Mathématique de France 182, 14–26 (2024). In French.
- G. Dubach. On the number of cycles in commutators of random permutations. The Annals of Applied Probability 34(4), 4072–4084 (2024).
- G. Dubach, J. Reker. Dynamics of a rank-one multiplicative perturbation of a unitary matrix. Random Matrices: Theory and Applications 13(2), 2450007 (2024).
- L.-P. Arguin, G. Dubach, L. Hartung. Maxima of a random model of the Riemann zeta function over intervals of varying length. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 60(1), 588–611 (2024).
- T. Lucas, G. Dubach. Counting Boiotians: Conscription Lists, Military Forces, and Demography in Hellenistic Boiotia. Hesperia 92(3), 481–513 (2023).
- G. Dubach, P. Germain, B. Harrop-Griffiths. On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model. Ars Inveniendi Analytica, Paper No. 7 (2023).
- G. Dubach, L. Erdős. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability 28, 1–13 (2023).
- G. Dubach. Explicit formulas concerning eigenvectors of weakly non-unitary matrices. Electronic Communications in Probability 28, 1–11 (2023).
- A. Serebryakov, N. Simm, G. Dubach. Characteristic polynomials of random truncations: moments, duality and asymptotics. Random Matrices: Theory and Applications 12(1), 2250049 (2023).
- G. Dubach. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability 26, 1–29 (2021).
- G. Dubach, Y. Peled. On words of non-Hermitian random matrices. The Annals of Probability 49(4), 1886–1916 (2021).
- G. Dubach. Symmetries of the quaternionic Ginibre ensemble. Random Matrices: Theory and Applications 10(1), 2150013 (2021).
- G. Dubach, F. Mühlböck. Formal verification of Zagier's one-sentence proof. Preprint, arXiv:2103.11389 (2021).
- P. Bourgade, G. Dubach. The distribution of overlaps between eigenvectors of Ginibre matrices. Probability Theory and Related Fields 177, 397–464 (2020).
- G. Dubach. Powers of Ginibre eigenvalues. Electronic Journal of Probability 23, 1–31 (2018).
Supervision
Postdoctoral researcher
- Stéphane Dartois, now a professeur junior at Université de Bordeaux.
PhD students
- Aniss Fares (since September 2024, co-supervised with Alice Guionnet).
- Domitille Saliou (since October 2026, co-supervised with Joseph Najnudel).
Masters' theses (stages et mémoires de M2)
- Aniss Fares (2024).
- Roberto Bolzan (2026).
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