Research

My research interests lie in the field of High-Dimensional Probability Theory, in particular:
  • Free Probability Theory
  • Random Matrix Theory
  • Matrix concentration inequalities
  • Mathematical aspects of deep learning and neural networks
  • Weak Dependence
Publications and Preprints:
  • The Distribution of Polynomials in Monotone Independent Elements. 
    Joint work with P-L. Tseng.
    To appear in: Random Matrices: Theory and Applications.     arXiv: arXiv:2311.05979
  • Quantitative Estimates for Operator-Valued and Infinitesimal Boolean and Monotone Limit Theorems. 
    Joint work with O. Arizmendi and P-L. Tseng.
    To appear in: Indiana University Mathematics Journal. arXiv: arXiv:2211.08054 
  • Berry-Esseen bounds for the multivariate B-free CLT and operator-valued matrices. 
    Joint work with T. Mai.
    Transactions of the American Mathematical Society, 376 (2023), 3761-3818. AMS – arXiv 
  • Matrix Poincaré Inequalities and Concentration. 
    Joint work with R. Aoun and P. Youssef.
    Advances in Mathematics, 371, 107251, 2020. Elsevier – arXiv 
  • Operator-valued matrices with free or exchangeable entries. 
    Joint work with G. Cébron.
     Annales de l’Institut Henri Poincaré, 59(1): 503-537, 2023. Project Euclid –  arXiv  
  • Hölder continuity of cumulative distribution functions for noncommutative polynomials under finite free Fisher information.  
    Joint work with T. Mai.
    Journal of Functional Analysis, 279(8):108710, 45, 2020. Elsevier – arXiv 
  • A CLT for linear spectral statistics of large random information-plus-noise matrices. 
    Joint work with J. Najim and J. Yao.
    Stochastic Processes and their Applications, 130(4): 2250–2281, 2020    . Elsevier – HAL 
  • Bernstein-type inequality for a class of dependent random matrices.
    Joint work with F. Merlevède  and P. Youssef.
    Random Matrices: Theory and Applications, 5 (02), 1650006, 2016. World Scientific – arXiv 
  • Limiting spectral distribution of Gram matrices associated with functionals of β-mixing processes. 
    Journal of Mathematical Analysis and Applications, 433(1):416 — 433, 2016. Elsevier –  arXiv 
  • On the limiting spectral distribution for a large class of symmetric random matrices with correlated entries. 
    Joint work with F. Merlevède and M. Peligrad.
    Stochastic Processes and their Applications, 125(7):2700 — 2726, 2015. Elsevier – PDF 
  • Limiting spectral distribution of large sample covariance matrices associated with a class of stationary processes. 
    Joint work with F. Merlevède.
    Journal of Theoretical Probability, pages 1–39, 2013. Springer – PDF