
Open access
Date
2014-06-30Type
- Journal Article
Citations
Cited 11 times in
Web of Science
Cited 11 times in
Scopus
ETH Bibliography
yes
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Abstract
We numerically show that the statistical properties of the shortest path on critical percolation clusters are consistent with the ones predicted for Schramm-Loewner evolution (SLE) curves for κ = 1.04 ± 0.02. The shortest path results from a global optimization process. To identify it, one needs to explore an entire area. Establishing a relation with SLE permits to generate curves statistically equivalent to the shortest path from a Brownian motion. We numerically analyze the winding angle, the left passage probability, and the driving function of the shortest path and compare them to the distributions predicted for SLE curves with the same fractal dimension. The consistency with SLE opens the possibility of using a solid theoretical framework to describe the shortest path and it raises relevant questions regarding conformal invariance and domain Markov properties, which we also discuss. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000086406Publication status
publishedExternal links
Journal / series
Scientific ReportsVolume
Pages / Article No.
Publisher
Nature Publishing GroupSubject
Statistical physics; Phase transitions and critical phenomenaOrganisational unit
03733 - Herrmann, Hans Jürgen (emeritus) / Herrmann, Hans Jürgen (emeritus)
Funding
319968 - Fluid Flow in Complex and Curved Spaces (EC)
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Show all metadata
Citations
Cited 11 times in
Web of Science
Cited 11 times in
Scopus
ETH Bibliography
yes
Altmetrics