Ahmed Bou-Rabee

activity

20192026

most citedConvergence of the random Abelian sandpile

5 citations · 10 across the 14 of their papers we have counts for

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8 papers · 1 filter

math.PR2026

Limit shapes for centrally excited walks

Ahmed Bou-Rabee, Yuval Peres, Tuan-Minh Nguyen +1

A centrally excited random walk on $Z^{d}$ 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.…

math.PR2026

Once-reinforced random walk on $Z^{d}$ has range exponent at least $d / (d + 1)$

Ahmed Bou-Rabee, Yuval Peres

In once-reinforced random walk, introduced by Davis (1990), every edge starts with weight one and is assigned weight $β \geq 1$ after its first crossing. At each step the walker choo…

math.PR2026

The randomly oriented Manhattan lattice in 2D is transient

Ahmed Bou-Rabee, Yuval Peres

Independently orient each horizontal and vertical line of $Z^{2}$ by a fair coin. A walker chooses one of the two lines through its current position with equal probability a…

math.PR2026

Quantitative explosion and percolation of the divisible sandpile

Ahmed Bou-Rabee, Christoforos Panagiotis

The divisible sandpile on $Z^{d}$ 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…

math.PR2026

Sharpness and critical scaling of parking

Ahmed Bou-Rabee, Christoforos Panagiotis

In the parking model, each site of the $d$ -dimensional lattice independently starts with one car with probability $p$ or one parking spot with probability $1 - p$ . Cars move accordin…

math.PR2026

Eulerian walkers on $Z^{2}$ have range exponent $2/3$

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…

math.PR2026

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…

math.PR2026

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 $R^{d}$ , $d \geq 2$ , subject to molecular diffusion and advection by a random incompressible flow. The velocity field is the…

Limit shapes for centrally excited walks

Once-reinforced random walk on Zd has range exponent at least d/(d+1)

The randomly oriented Manhattan lattice in 2D is transient

Quantitative explosion and percolation of the divisible sandpile

Sharpness and critical scaling of parking

Eulerian walkers on Z2 have range exponent 2/3

Divisible sandpiles via random walks in random scenery

Superdiffusion and anomalous regularization in self-similar random incompressible flows

Once-reinforced random walk on $Z^{d}$ has range exponent at least $d / (d + 1)$

Eulerian walkers on $Z^{2}$ have range exponent $2/3$