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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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