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A survey of fractal features of Bernoulli percolation

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  • Balankin, Alexander S.

Abstract

This work is devoted to the fractal features of Bernoulli percolation in different space dimensions. The focus is made on the fractal attributes associated with the connectivity, ramification, and loopiness of percolation clusters and their substructures. In this way we ascertain a connection between the connectivity dimension and topological invariants. Consequently we elucidate the difference between the fractal dimensions of the minimum path and the geodesic on the percolation cluster. We also derive a relation between the topological Hausdorff dimension of percolation cluster and the correlation length exponent. Further we establish that the percolation cluster and its hull have the same topological Hausdorff dimension. These findings allow us to found the ranges for admissible values of dimension numbers characterizing the percolation cluster and their substructures in different space dimensions. Thus we scrutinize the data of numerical simulations.

Suggested Citation

  • Balankin, Alexander S., 2024. "A survey of fractal features of Bernoulli percolation," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005964
    DOI: 10.1016/j.chaos.2024.115044
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    References listed on IDEAS

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