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arXiv · 1206.3159

Watersheds are Schramm-Loewner Evolution curves

E. Daryaei·N. A. M. Araujo·K. J. Schrenk·S. Rouhani·H. J. Herrmann
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Abstract

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 SLE$_κ$, with $κ=1.734\pm0.005$, 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 (CFT) with central charge $c\approx-7/2$.

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E. Daryaei, N. A. M. Araujo, K. J. Schrenk, S. Rouhani, H. J. Herrmann. 2012-12-03. Watersheds are Schramm-Loewner Evolution curves. https://doi.org/10.1103/physrevlett.109.218701

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