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Scaling limit of the random walk among random traps on $$\mathbb Z^{d}$$. (English. French summary) Zbl 1262.60098
Summary: Attributing a positive value $$\tau _{x}$$ to each $$x\in \mathbb Z^{d}$$, 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 $$d\geq 5$$. 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 the 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.

##### MSC:
 60K37 Processes in random environments 60G52 Stable stochastic processes 60F17 Functional limit theorems; invariance principles 82D30 Statistical mechanical studies of random media, disordered materials (including liquid crystals and spin glasses)
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