Watersheds are Schramm-Loewner Evolution Curves
Kabir Ramola, Post-Doc LPTMS
SLE has grown in prominence over the last decade and has helped unify several aspects of critical phenomena, percolation theory and conformal field theory. This paper discusses an interesting real world application of this somewhat technical subject.
E. Daryaei, N. A. M. Arau´jo, K. J. Schrenk, S. Rouhani, and H. J. Herrmann
Abstract of the article : We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner evolution (SLE) curves, being described by one single parameter κ. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLEκ, with κ=1.734±0.005, being the only known physical example of an SLE with κ<2. This lies outside the well-known duality conjecture, bringing up new questions regarding the existence and reversibility of dual models. Furthermore, it constitutes a strong indication for conformal invariance in random landscapes and suggests that watersheds likely correspond to a logarithmic conformal field theory with a central charge c≈-7/2.