Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

                     
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Séminaire de groupe

Watersheds are Schramm-Loewner evolution curves
Shahin Rouhani
Physics Department, Sharif University of Technology, Téhéran (Iran)
jeudi 07 novembre 2013 , 10h25
Salle de séminaire du groupe de Physique Statistique

I shall argue that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner evolution (SLE) curves, being described by one single parameter $\kappa$. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLE${}_\kappa$, with $\kappa=1.734\pm 0.005$, being the only known physical example of an SLE with $\kappa<2$. 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 $c\simeq -7/2$. I further argue that numerical evidence suggests that Loop Erased Random Walks (LERW) on critical percolation clusters, fall into the same universality class.



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