Publications
- G. Dubach, J. Reker, Dynamics of a rank one multiplicative perturbation of a Unitary matrix, to appear in Random Matrices: Theory and Applications (2024).
- G. Dubach, On the number of cycles in commutators of random permutations, to appear in Annals of Applied Probability (2024).
- G. Dubach, P. Germain, B. Harrop-Griffiths, On the derivation of the homogeneous kinetic wave equation for a non-linear random matrix model ,
Ars Inveniendi Analytica (2023), Paper No. 7.
- 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).
- L.-P. Arguin, G. Dubach, L. Hartung, Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length , to appear in Annales de L'Institut Henri Poincaré (2022).
- A. Serebryakov, N. Simm, G. Dubach, Characteristic polynomials of random truncations: moments, duality and asymptotics, to appear in Random Matrices: Theory and Applications (2022).
- T. Lucas, G. Dubach, Counting Boeotians: Conscription Lists, Military Forces and Demography in Hellenistic Boeotia (255-171 B.C.), to appear in Hesperia : the Journal of the American School of Classical Studies at Athens.
- G. Dubach, On eigenvector stastistics 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 (2021) 1886-1916.
- G. Dubach, Symmetries of the Quaternionic Ginibre Ensemble, Random Matrices: Theory and Applications (2020) 2150013.
- P. Bourgade, G. Dubach, The distribution of overlaps between eigenvectors of Ginibre matrices, Probability Theory and Related Fields (2020) 177: 397-464.
- G. Dubach, Powers of Ginibre Eigenvalues, Electronic Journal of Probability 23, 1-31 (2018).
Coming soon
- P. Deift, G. Dubach, C. Tomei, T. Trogdon, The Toda lattice and the eigenvalue problem for random Hermitian matrices (book, in prep.)
- P. Bourgade, G. Dubach, L. Hartung, Fisher-Hartwig asymptotics for non-Hermitian random matrices, in prep.
Formal verification
Zagier's one-sentence proof of Fermat's two squares theorem, with F. Muehlboeck.
Current code available on github.com/gdubach/Zagier_project.
Companion paper:
Formal verification of Zagier's one-sentence proof (2021)
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