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May 2019 Capacity of the range of random walk on $\mathbb{Z}^{4}$
Amine Asselah, Bruno Schapira, Perla Sousi
Ann. Probab. 47(3): 1447-1497 (May 2019). DOI: 10.1214/18-AOP1288

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.

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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

Information

Received: 1 January 2017; Revised: 1 March 2018; Published: May 2019
First available in Project Euclid: 2 May 2019

zbMATH: 07067274
MathSciNet: MR3945751
Digital Object Identifier: 10.1214/18-AOP1288

Subjects:
Primary: 60F05
Secondary: 60G50

Keywords: capacity , central limit theorem , Green kernel , Law of Large Numbers

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 3 • May 2019
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