Abstract
We study the scaling limit of the capacity of the range of a 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 [Comm. Math. Phys. 104 (1986) 471–507] for the volume of the range in dimension two.
Citation
Amine Asselah. Bruno Schapira. Perla Sousi. "Capacity of the range of random walk on $\mathbb{Z}^{4}$." Ann. Probab. 47 (3) 1447 - 1497, May 2019. https://doi.org/10.1214/18-AOP1288
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