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Capacity of the range of random walk on $\mathbb{Z}^4$

We study the scaling limit of the capacity of the range of a simple random 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 for the volume of the range in dimension two.

preprint2016arXivOpen access
Amine AsselahBruno SchapiraPerla Sousi
math.PR
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Open access3 authors1 topic
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Amine AsselahBruno SchapiraPerla Sousi

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