6 papers
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…