Fractal dimension of discrete sets and percolation

2019/11/05 by Heydenreich, Markus
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1911.01765

Abstract

There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of \mathbb R^d. In this expository text, we discuss their analogues for infinite subsets of \mathbb Z^d and, more generally, for infinite graphs. We then apply these notions to critical percolation clusters, where the various dimensions have different values.

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