Aging and spin-glass dynamics (2003)
We survey the recent mathematical results about aging in certain simple disordered models. We start by the Bouchaud trap model. We then survey the results obtained for simple models of spin-glass...
Multi-scale homogenization with bounded ratios and Anomalous Slow Diffusion (2001)
Ben-Arous, Gérard, Owhadi, Houman
We show that the effective diffusivity matrix $D(V^n)$ for the heat operator $\partial_t-(\Delta/2-\nabla V^n \nabla)$ in a periodic potential $V^n=\sum_{k=0}^n U_k(x/R_k)$ obtained as a...
Super-diffusivity in a shear flow model from perpetual homogenization (2001)
Ben-Arous, Gérard, Owhadi, Houman
This paper is concerned with the asymptotic behavior solutions of stochastic differential equations $dy_t=d\omega_t -\nabla \Gamma(y_t) dt$, $y_0=0$ and $d=2$. $\Gamma$ is a $2\times 2$...