CAPACITY OF THE RANGE OF RANDOM WALK ON Z^4
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Asselah, Amine
Schapira, Bruno
Sousi, Perla
Abstract
We study the scaling limit of the capacity of the range of a ran- dom walk on the integer lattice in dimension four. We establish a strong law of large numbers and a central limit theorem with a non-gaussian limit. The asymptotic behaviour is analogous to that found by Le Gall in ’86 [28] for the volume of the range in dimension two.
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Annals of Probability
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Institute of Mathematical Statistics