LUCAS BENIGNI

I am an Assistant Professor in the mathematics and statistics department of the Université de Montréal. Before that, I was an L. E. Dickson Instructor at the University of Chicago. I obtained my PhD from Université Paris-Diderot in 2019 under the supervision of Sandrine Péché (LPSM) and Paul Bourgade (CIMS, New York University).

You can read my PhD thesis here.

My research interests lie in probability theory, statistical physics, stochastic processes. I am more specifically interested in the study of spectral elements of large random matrices and its applications to mathematical physics or machine learning.

Here is my detailed CV.

Email: lucas.benigni@umontreal.ca

Telephone: +1 514-343-7452

Papers and preprints:

Address: Département de mathématiques et de statistique

Pavillon André-Aisenstadt

2920 Chemin de la tour, local AA-5190

Montréal (Québec) H3T 1J4

- Fluctuations of eigenvector overlaps and the Berry conjecture for Wigner matrices, with G. Cipolloni, preprint 2022
- Largest eigenvalues of the Conjugate Kernel of single-layered neural networks, with S. Péché, preprint 2022
- Determinantal structures for Bessel fields, with P.-K. Hung and X. Wu, preprint 2021
- Fluctuations in local quantum unique ergodicity for generalized Wigner matrices, with P. Lopatto, Comm. Math. Phys. 391 (2022), 401-454.
- Optimal delocalization for generalized Wigner matrices, with P. Lopatto, Adv. Math. 396 (2022), 108109.
- Eigenvalue distribution of nonlinear models of random matrices, with S. Péché, Electron. J. Probab. 26 (2021), 1-37.
- Fermionic eigenvector moment flow, Probab. Theory Related Fields 179 (2021),733-775.
- Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices, Ann. Inst. Henri Poincaré Probab. Stat. 56 (4) (2020), 2822-2867.
- Hausdorff dimension of the record set of a fractional Brownian motion, with C. Cosco, A. Shapira, and K. J. Wiese, Electron. Commun. Probab. 23 (2018), paper no. 22, 8pp.