Scaling limit for trap models on $\mathbb{Z}^d$

We give the ``quenched'' scaling limit of Bouchaud's trap model in ${d\ge 2}$. This scaling limit is the fractional-kinetics process, that is the time change of a $d$-dimensional Brownian motion by the inverse of an independent $\alpha$-stable subordinator.

Gérard Ben Arous, Jiří Černý · 2006