Mathematics – Probability
Scientific paper
2011-04-11
Mathematics
Probability
28 pages, 3 figures, Title changed, some proof simplified, to appear in AIHP
Scientific paper
We study trajectories of d-dimensional Brownian Motion in Poissonian potential up to the hitting time of a distant hyper-plane. Our Poissonian potential V can be associated to a field of traps whose centers location is given by a Poisson Point process and whose radii are IID distributed with a common distribution that has unbounded support; it has the particularity of having long-range correlation. We focus on the case where the law of the trap radii has power-law decay and prove that superdiffusivity hold under certain condition, and get a lower bound on the volume exponent. Results differ quite much with the one that have been obtained for the model with traps of bounded radii by W\"uhtrich: the superdiffusivity phenomenon is enhanced by the presence of correlation.
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