Open Access
2018 The dimension of the range of a transient random walk
Nicos Georgiou, Davar Khoshnevisan, Kunwoo Kim, Alex D. Ramos
Electron. J. Probab. 23: 1-31 (2018). DOI: 10.1214/18-EJP201


We find formulas for the macroscopic Minkowski and Hausdorff dimensions of the range of an arbitrary transient walk in $\mathbb{Z} ^d$. This endeavor solves a problem of Barlow and Taylor (1991).


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Nicos Georgiou. Davar Khoshnevisan. Kunwoo Kim. Alex D. Ramos. "The dimension of the range of a transient random walk." Electron. J. Probab. 23 1 - 31, 2018.


Received: 21 December 2017; Accepted: 18 July 2018; Published: 2018
First available in Project Euclid: 12 September 2018

zbMATH: 06964777
MathSciNet: MR3858911
Digital Object Identifier: 10.1214/18-EJP201

Primary: 60G50
Secondary: 60J45 , 60J80

Keywords: capacity , fractal percolation , Hausdorff dimension , recurrent sets , transient random walks

Vol.23 • 2018
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