# Scaling limit of the random walk among random traps on Z^d Source: [Scaling limit of the random walk among random traps on Z^d]() Collection index: [llms.txt]() Data updated: 2025-10-25T11:35:08.305Z Authors: Jean-Christophe Mourrat Published: 2010-01-14T14:03:53.000Z ## Abstract Attributing a positive value \\tau\_x to each x in Z^d, we investigate a nearest-neighbour random walk which is reversible for the measure with weights (\\tau\_x), often known as "Bouchaud's trap model". We assume that these weights are independent, identically distributed and non-integrable random variables (with polynomial tail), and that d \> 4. We obtain the quenched subdiffusive scaling limit of the model, the limit being the fractional kinetics process. We begin our proof by expressing the random walk as a time change of a random walk among random conductances. We then focus on proving that the time change converges, under the annealed measure, to a stable subordinator. This is achieved using previous results concerning the mixing properties of the environment viewed by the time-changed random walk. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()