Research

My topic of researchi are probability and mathematical physics. Most of my results are about random graphs and random matrices

Publications

  • R Rivier and RD, Spectral gap and embedded trees for the Laplacian of the Erdos-Renyi graph arXiv:2309.17292, 2023.
  • RD, For the use of exterior form in daily physics, an introduction without coordinate frame arXiv:2307.06597, 2023.
  • J Alt, RD and A Knowles, Localized phase for the Erdos-Rényi graph arXiv:2305.16294, 2023.
  • N Cook, RD and A Guionnet Full large deviation principles for the largest eigenvalue of sub-Gaussian Wigner matrices arXiv:2302.14823, 2023.
  • RD, Analysis of the one dimensional inhomogeneous Jellium model with the Birkhoff-Hopf Theorem (revision requested in Journal of Functional Analysis) arXiv:1806.07681, 2018.
  • J Alt, RD and A Knowles, Poisson statistics and localization at the spectral edge of sparse Erdös–Rényi graphs, arXiv:2106.12519, 2021.
  • J Alt, RD and A Knowles, The completely delocalized region of the Erdös-Renyi graph, accepted in Electronic Communications in Probability, arXiv:2005.14180, 2021.
  • J Alt, RD and A Knowles, Delocalization transition for critical Erdös-Rényi graphs, accepted in Communications in Mathematical Physics, arXiv:2005.14180, 2020.
  • J Alt, RD and A Knowles, Extremal eigenvalues of critical Erdös-Rényi graphs, Annals of Probability. arXiv:1905.03243, 2019.
  • RD, Foward Backward process for one dimension Anderson model, Electronic Communication of Probability, arXiv:1711.11302, 2017.
  • RD and F Huveneers, Periodically driven Anderson model, Annales Henri Poincare, arXiv:1607.07353, 2017.
  • RD, Anderson localization for infinitely many interacting particles under Hartree Fock theory, Journal of Spectral Theory, arXiv:1602.02896, 2016.

PhD Thesis

  • RD, Analyse mathématique de divers systèmes de particules en milieu désordonné. tel-01886142

Popular Science Article

  • RD, Une version simplifiée du Théorème de Gauss-Bonnet. Image des Maths