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The dimension of the range of a transient random walk. (English) Zbl 1414.60028
Summary: 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 M. T. Barlow and S. J. Taylor [Proc. Lond. Math. Soc. (3) 64, No. 1, 125–152 (1992; Zbl 0753.28006)].

MSC:
60G50 Sums of independent random variables; random walks
60J45 Probabilistic potential theory
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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