Ahmed Bou-Rabee

Courant Institute
Department of Mathematics
Office: 1007 Warren Weaver Hall
Email:   ahmedmb@gmail.com

I am an NSF Postdoctoral Fellow at the Courant Institute sponsored by Scott Armstrong. I began my fellowship at Cornell University sponsored by Lionel Levine. I received my PhD at the University of Chicago under the supervision of Charles K. Smart in June 2022. Previously, I received a B.S. in mathematics and an M.S. in statistics from Stanford University.

I am interested in probability and partial differential equations. Some topics I have worked on include quantitative stochastic homogenization, the Abelian sandpile, and Liouville quantum gravity.

Publications and Preprints

  1. Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift, with Scott Armstrong and Tuomo Kuusi. [arXiv:2404.01115] [Blog]
  2. Unique continuation on planar graphs, with Bill Cooperman and Shirshendu Ganguly. [arXiv:2309.13728]
  3. Rigidity of harmonic functions on the supercritical percolation cluster, with Bill Cooperman and Paul Dario. [arXiv:2303.04736]
  4. Internal DLA on mated-CRT maps, with Ewain Gwynne. Annals of Probability, to appear. [arXiv:2211.04891]
  5. Harmonic balls in Liouville quantum gravity, with Ewain Gwynne. [arXiv:2208.11795]
  6. Integer superharmonic matrices on the F-lattice. Advances in Mathematics, 436, 109400 (2024). [Journal] [arxiv:2110.07556] [Extended Appendix] [Code]
  7. Hamilton-Jacobi scaling limits of Pareto peeling in 2D, with Peter S. Morfe. Probability Theory and Related Fields, 188, 235-307 (2024). [Journal] [arXiv:2110.06016] [Code]
  8. A shape theorem for exploding sandpiles. Annals of Applied Probability 34(1A): 714-742 (2024) [Journal] [arxiv:2102.04422] [Notebook]
  9. Dynamic dimensional reduction in the Abelian sandpile. Communications in Mathematical Physics , 390, 933-958 (2022). [Journal] [arxiv:2009.05968] [Code]
  10. Convergence of the random Abelian sandpile. Annals of Probability 49(6): 3168-3196 (2021). [Journal] [arxiv:1909.07849] [Pictures]