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Transactions of the American Mathematical Society

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


Authors: Amine Asselah, Bruno Schapira and Perla Sousi
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 60F05, 60G50
DOI: https://doi.org/10.1090/tran/7247
Published electronically: April 25, 2018
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Abstract: We study the capacity of the range of a transient simple random walk on $ \mathbb{Z}^d$. Our main result is a central limit theorem for the capacity of the range for $ d\ge 6$. We present a few open questions in lower dimensions.


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Amine Asselah
Affiliation: Aix-Marseille Université – and – Université Paris-Est Créteil, Laboratoire d’Analyse et de Mathématiques Appliquées, Bât. P2, 94010 Créteil Cedex, France
Email: amine.asselah@u-pec.fr

Bruno Schapira
Affiliation: Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France
Email: bruno.schapira@univ-amu.fr

Perla Sousi
Affiliation: University of Cambridge, Cambridge, Department of Pure Mathematics, CB3 OWB, United Kingdom
Email: p.sousi@statslab.cam.ac.uk

DOI: https://doi.org/10.1090/tran/7247
Keywords: Capacity, Green kernel, Lindeberg-Feller central limit theorem.
Received by editor(s): February 10, 2016
Received by editor(s) in revised form: January 12, 2017
Published electronically: April 25, 2018
Additional Notes: We thank the Institute IMéRA in Marseille for its hospitality.
This work has been carried out thanks partially to the support of A$^{*}$MIDEX grant (ANR-11-IDEX-0001-02) funded by the French Government “Investissements d’Avenir” program.
Article copyright: © Copyright 2018 American Mathematical Society

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