Cartesian products of the Sierpiński carpet (and similar self-similar fractals) with itself at least twice do not attain their conformal dimension.
arXiv preprint arXiv:2408.15692 , year=
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The paper proves Gromov-Hausdorff-Prokhorov-Skorokhod convergence of random walks on EIGS fractal graphs to diffusion and solves the open DHL percolation cluster problem.
Extends Edge Iterated Graph Systems to reducible cases with new definitions and proofs that multiscale-freeness and multifractality have finite discrete spectra.
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Cartesian products of Sierpi\'nski carpets do not attain their conformal dimension
Cartesian products of the Sierpiński carpet (and similar self-similar fractals) with itself at least twice do not attain their conformal dimension.
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Iterated Graph Systems (I): random walks and diffusion limits
The paper proves Gromov-Hausdorff-Prokhorov-Skorokhod convergence of random walks on EIGS fractal graphs to diffusion and solves the open DHL percolation cluster problem.
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Reducible Iterated Graph Systems: multiscale-freeness and multifractals
Extends Edge Iterated Graph Systems to reducible cases with new definitions and proofs that multiscale-freeness and multifractality have finite discrete spectra.