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. Unique continuation on planar graphs, with Bill Cooperman and Shirshendu Ganguly. [arXiv:2309.13728]
  2. Rigidity of harmonic functions on the supercritical percolation cluster, with Bill Cooperman and Paul Dario. [arXiv:2303.04736]
  3. Internal DLA on mated-CRT maps, with Ewain Gwynne. [arXiv:2211.04891]
  4. Harmonic balls in Liouville quantum gravity, with Ewain Gwynne. [arXiv:2208.11795]
  5. Integer superharmonic matrices on the F-lattice. To appear in Advances in Mathematics. [arxiv:2110.07556] [Extended Appendix] [Code]
  6. Hamilton-Jacobi scaling limits of Pareto peeling in 2D, with Peter S. Morfe. To appear in Probability Theory and Related Fields. [arXiv:2110.06016] [Code]
  7. A shape theorem for exploding sandpiles. To appear in Annals of Applied Probability. [arxiv:2102.04422] [Notebook]
  8. Dynamic dimensional reduction in the Abelian sandpile. Communications in Mathematical Physics, 390, 933-958 (2022). [Journal] [arxiv:2009.05968] [Code]
  9. Convergence of the random Abelian sandpile. Annals of Probability 49(6): 3168-3196 (2021). [Journal] [arxiv:1909.07849] [Pictures]