Ahmed Bou-Rabee

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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…

math.PR2024

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 $R^{d}$ advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetri…