Shortest path and Schramm-Loewner Evolution View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-05

AUTHORS

N Posé, K J Schrenk, N A M Araújo, H J Herrmann

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. More... »

PAGES

5495

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1038/srep05495

DOI

http://dx.doi.org/10.1038/srep05495

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1019231861

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/24975019


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