5 citations · 10 across the 14 of their papers we have counts for
16 papers
Limit shapes for centrally excited walks
Ahmed Bou-Rabee, Yuval Peres, Tuan-Minh Nguyen +1
A centrally excited random walk on moves like simple random walk, except that its first step from each site other than the origin has a drift of fixed size toward it.…
Once-reinforced random walk on has range exponent at least
Ahmed Bou-Rabee, Yuval Peres
In once-reinforced random walk, introduced by Davis (1990), every edge starts with weight one and is assigned weight after its first crossing. At each step the walker choo…
The randomly oriented Manhattan lattice in 2D is transient
Ahmed Bou-Rabee, Yuval Peres
Independently orient each horizontal and vertical line of by a fair coin. A walker chooses one of the two lines through its current position with equal probability a…
Quantitative explosion and percolation of the divisible sandpile
Ahmed Bou-Rabee, Christoforos Panagiotis
The divisible sandpile on starts from i.i.d. masses at each site, and, in each discrete time step, a site with mass above one keeps one unit and sends the excess equ…
Sharpness and critical scaling of parking
Ahmed Bou-Rabee, Christoforos Panagiotis
In the parking model, each site of the -dimensional lattice independently starts with one car with probability or one parking spot with probability . Cars move accordin…
Eulerian walkers on have range exponent
Ahmed Bou-Rabee, Yuval Peres
In the Eulerian walker model (also known as rotor walk), each site of the square lattice begins with an arrow pointing to one of its four neighbors. A walker that starts at the ori…
Divisible sandpiles via random walks in random scenery
Ahmed Bou-Rabee, Yuval Peres, Ecaterina Sava-Huss
We analyze an optimal stopping problem for random walk in random scenery on general graphs, and determine when it has a finite optimum. We use this to extend a theorem of Levine, M…
Superdiffusion and anomalous regularization in self-similar random incompressible flows
Scott Armstrong, Ahmed Bou-Rabee, Tuomo Kuusi
We study the long-time behavior of a particle in , , subject to molecular diffusion and advection by a random incompressible flow. The velocity field is the…
Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift
Scott Armstrong, Ahmed Bou-Rabee, Tuomo Kuusi
We consider the long-time behavior of a diffusion process on advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetri…
Unique continuation on planar graphs
Ahmed Bou-Rabee, William Cooperman, Shirshendu Ganguly
We show that a discrete harmonic function which is bounded on a large portion of a periodic planar graph is constant. A key ingredient is a new unique continuation result for the w…
Rigidity of harmonic functions on the supercritical percolation cluster
Ahmed Bou-Rabee, William Cooperman, Paul Dario
We use ideas from quantitative homogenization to show that nonconstant harmonic functions on the percolation cluster cannot satisfy certain structural constraints, for example, a L…
Integer superharmonic matrices on the -lattice
Ahmed Bou-Rabee
We prove that the set of quadratic growths achievable by integer superharmonic functions on the -lattice, a periodic subgraph of the square lattice with oriented edges, has the…
Hamilton-Jacobi scaling limits of Pareto peeling in 2D
Ahmed Bou-Rabee, Peter S. Morfe
Pareto hull peeling is a discrete algorithm, generalizing convex hull peeling, for sorting points in Euclidean space. We prove that Pareto peeling of a random point set in two dime…
A shape theorem for exploding sandpiles
Ahmed Bou-Rabee
We study scaling limits of exploding Abelian sandpiles using ideas from percolation and front propagation in random media. We establish sufficient conditions under which a limit sh…
Dynamic dimensional reduction in the Abelian sandpile
Ahmed Bou-Rabee
We prove the dimensional reduction conjecture of Fey, Levine, and Peres (2010) on the hypercube. The proof shows that dimensional reduction, symmetry, and regularity of the Abelian…
Convergence of the random Abelian sandpile
Ahmed Bou-Rabee
We prove that Abelian sandpiles with random initial states converge almost surely to unique scaling limits. The proof follows the Armstrong-Smart program for stochastic homogenizat…