title: Shortest path and Schramm-Loewner evolution.
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.
authors: Computational Physics for Engineering Materials, IfB, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland.
authors: N
authors: N
authors: Posé
authors: Computational Physics for Engineering Materials, IfB, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland.
authors: K J
authors: KJ
authors: Schrenk
authors: Computational Physics for Engineering Materials, IfB, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland.
authors: N A M
authors: NA
authors: Araújo
authors: 1] Computational Physics for Engineering Materials, IfB, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland [2] Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil.
authors: H J
authors: HJ
authors: Herrmann