We give the “quenched” scaling limit of Bouchaud’s trap model in d≥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 α-stable subordinator.
"Scaling limit for trap models on ℤd." Ann. Probab. 35 (6) 2356 - 2384, November 2007. https://doi.org/10.1214/009117907000000024