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arXiv · 1911.01765

Fractal dimension of discrete sets and percolation

Markus Heydenreich
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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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Markus Heydenreich. 2019-11-05. Fractal dimension of discrete sets and percolation. https://arxiv.org/abs/1911.01765

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