caa a22 4500 528786172 20181217030314.0 cr unu---uuuuu 180924e20140630xx s 000 0 eng 10.3929/ethz-b-000086406 doi 10.1038/srep05495 doi (ETHRESEARCH)oai:www.research-collection.ethz.ch:20.500.11850/86406 Shortest path and Schramm-Loewner Evolution [Elektronische Daten] [Nicolas Posé, K. Julian Schrenk, Nuno A.M. Araújo, Hans J. Herrmann] Sci Rep Open access ethresearch 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. Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International http://creativecommons.org/licenses/by-nc-sa/4.0 ethresearch Statistical physics ethresearch Phase transitions and critical phenomena ethresearch Posé Nicolas joint author Schrenk K. Julian joint author Araújo Nuno A.M. joint author Herrmann Hans J. joint author Scientific Reports London : Nature Publishing Group 4, p. 5495 2045-2322 http://hdl.handle.net/20.500.11850/86406 text/html WWW-Backlink auf das Repository (Open access) 1 Journal Article ethresearch ETHRESEARCH 856 40 http://hdl.handle.net/20.500.11850/86406 text/html WWW-Backlink auf das Repository (Open access) ETHRESEARCH 700 1- Posé Nicolas joint author ETHRESEARCH 700 1- Schrenk K. Julian joint author ETHRESEARCH 700 1- Araújo Nuno A.M. joint author ETHRESEARCH 700 1- Herrmann Hans J. joint author ETHRESEARCH 773 0- Scientific Reports London : Nature Publishing Group 4, p. 5495 2045-2322 BK010053 XK010053 XK010000 ETHRESEARCH ETHRESEARCH ETHRESEARCH Journal Article Open access