On the dynamics of trap models in Z^d

Details On the dynamics of trap models in Z^d On the dynamics of trap models in Z^d

2010-10-26

arxiv.org/abs/1010.5418v1

Mathematics

Probability

28 pages

Scientific paper

We consider stochastic processes in a random environment as follows. The environment is given by a family tau=(tau_x, x in Z^d) of positive iid random variables in the basin of attraction of an a-stable law, 0=2, and also many one dimensional random walks. We then derive aging results for our process, namely scaling limits for some its two-time correlation functions. The scaling limit results mentioned above are integrated results with respect to the environment. Under an additional condition on the size of the intersection of the ranges of two independent copies of the underlying random walk, roughly saying that it is relatively small compared to the range, we derive correspondingly stronger results,holding roughly in probability with respect to the environment.

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