Capacity of the range of random walk on 
Authors:
Amine Asselah, Bruno Schapira and Perla Sousi
Journal:
Trans. Amer. Math. Soc. 370 (2018), 7627-7645
MSC (2010):
Primary 60F05, 60G50
DOI:
https://doi.org/10.1090/tran/7247
Published electronically:
April 25, 2018
MathSciNet review:
3852443
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We study the capacity of the range of a transient simple random walk on 
. Our main result is a central limit theorem for the capacity of the range for 
. We present a few open questions in lower dimensions.
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Additional Information
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
