Topological Hausdorff dimension and geodesic metric of critical percolation cluster in two dimensions

DOI10.1016/j.physleta.2017.06.028zbMath1375.82048OpenAlexW2693014738WikidataQ60142097 ScholiaQ60142097MaRDI QIDQ1681639

Baltasar Mena, Alexander S. Balankin, M. A. Martínez-Cruz

Publication date: 24 November 2017

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2017.06.028

zbMATH Keywords

percolationscaling exponentsfractal geometrygeodesic metrictopological Hausdorff dimensiondimension numbers

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Percolation (82B43)

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Cites Work

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• Random walks on disordered media and their scaling limits. École d'Été de Probabilités de Saint-Flour XL -- 2010
• Recent advances in percolation theory and its applications
• The Alexander-Orbach conjecture holds in high dimensions
• Critical exponents for two-dimensional percolation
• Hausdorff dimensions for SLE\(_6\).
• Relations between different notions of degrees of freedom of a quantum system and its classical model
• A new fractal dimension: the topological Hausdorff dimension
• Statistical and finite size scaling behavior of the red bonds near the percolation threshold
• Geodesic distances and intrinsic distances on some fractal sets
• Critical percolation exploration path and \(\mathrm{SLE}_{6}\): a proof of convergence
• Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits
• Phase Transition and Fractals
• Universality classes in nonequilibrium lattice systems
• The critical point of fractal percolation in three and more dimensions
• Fractal geometry: what is it, and what does it do?
• Exact critical exponent for the shortest-path scaling function in percolation
• Absence of a stiffness instability for a model critical-wetting transition in three dimensions
• Topological conformal dimension
• A direct electrifying algorithm for backbone identification