The dimension of the range of a transient random walk

Georgiou, Nicos, Khoshnevisan, Davar, Kim, Kunwoo and Ramos, Alex (2018) The dimension of the range of a transient random walk. Electronic Journal of Probability, 23 (83). pp. 1-31. ISSN 1083-6489

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Abstract

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).

Item Type: Article
Keywords: Transient random walks; Hausdorff dimension; recurrent sets; fractal percolation; capacity.
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics > QA0274 Stochastic processes
Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics > QA0274.7 Markov processes. Markov chains
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Depositing User: Nicos Georgiou
Date Deposited: 03 Aug 2018 14:36
Last Modified: 08 Nov 2018 09:54
URI: http://sro.sussex.ac.uk/id/eprint/77530

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The flat edge in last passage percolationG2031EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCILEP/P021409/1