Abstract
In this paper, we generalize a theorem due to Telcs concerning random walks on infinite graphs, which describes the relation of random walk dimension, fractal dimension and resistance dimension. Moreover, we obtain a reasonable upper bound and lower bound on the hitting time in terms of resistance for some nice graphs. In fact, the conditions given in this paper are weaker than those obtained by A. Telcs.
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Partly supported by National Natural Science Foundation and State Educational Committee of China.
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Zhou, X.Y. Resistance dimension, random walk dimension and fractal dimension. J Theor Probab 6, 635–652 (1993). https://doi.org/10.1007/BF01049168
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DOI: https://doi.org/10.1007/BF01049168