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The dimension of the range of a transient random walk

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journal contribution
posted on 2023-06-09, 14:22 authored by Nicos GeorgiouNicos Georgiou, Davar Khoshnevisan, Kunwoo Kim, Alex Ramos
We find formulas for the macroscopic Minkowski and Hausdorff dimensions of the range of an arbitrary transient walk in the integer lattice. This endeavor solves a problem of Barlow and Taylor (1991).

Funding

The flat edge in last passage percolation; G2031; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/P021409/1

History

Publication status

  • Published

File Version

  • Published version

Journal

Electronic Journal of Probability

ISSN

1083-6489

Publisher

Institute of Mathematical Statistics

External DOI

Issue

83

Volume

23

Page range

1-31

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-08-03

First Open Access (FOA) Date

2018-08-03

First Compliant Deposit (FCD) Date

2018-08-02

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    University of Sussex (Publications)

    Categories

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    Keywords

    Transient random walks; Hausdorff dimension; recurrent sets; fractal percolation; capacity.

    Licence

    CC BY 4.0

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