4 papers
Quantitative Einstein relation for reversible diffusions in a random environment
Ahmed Bou-Rabee, Ruizhe Xu
The Einstein relation describes the response of a diffusing particle to a small constant external force. It states that, as the force tends to zero, the ratio of the limiting veloc…
Quantitative homogenization for the critical long-range random conductance model
Ahmed Bou-Rabee, Paul Dario
We consider the long-range random conductance model on at the critical exponent: the jump rate between sites and decays as ,…
Gaussian fluctuations for Internal DLA on cylinders
Ahmed Bou-Rabee, Vittoria Silvestri, Ariel Yadin
Internal DLA is a discrete random growth model describing growing clusters of particles. Its limiting shape and fluctuations are well understood when the underlying graph is the $d…
Random walk on sphere packings and Delaunay triangulations in arbitrary dimension
Ahmed Bou-Rabee, Ewain Gwynne
We prove that random walks on a family of tilings of d-dimensional Euclidean space, with a canonical choice of conductances, converge to Brownian motion modulo time parameterizatio…