The Watershed Model and Schramm-loewner Evolution, Ph.D. Dissertation Sharif University of Technology ; Rouhani, Shahin (Supervisor)
Abstract
Schramm Loewner evolution (SLE) is a one-parameter family of random simple curves in the complex plane introduced by Schramm in 1999 which is believed to describe the scaling limit of a variety of domain interfaces at criticality. This thesis is concerned with statistical properties of watersheds dividing drainage basins. The fractal dimension of this model is 1.22 which is consistent with the known fractal dimension for several important models such as Invasion percolation and minimum spanning trees (MST). We present numerical evidences that in the scaling limit this model are SLE curves with =1.73, being the only known physical example of an
SLE with <2. This lies outside the... Cataloging briefThe Watershed Model and Schramm-loewner Evolution, Ph.D. Dissertation Sharif University of Technology ; Rouhani, Shahin (Supervisor)
Abstract
Schramm Loewner evolution (SLE) is a one-parameter family of random simple curves in the complex plane introduced by Schramm in 1999 which is believed to describe the scaling limit of a variety of domain interfaces at criticality. This thesis is concerned with statistical properties of watersheds dividing drainage basins. The fractal dimension of this model is 1.22 which is consistent with the known fractal dimension for several important models such as Invasion percolation and minimum spanning trees (MST). We present numerical evidences that in the scaling limit this model are SLE curves with =1.73, being the only known physical example of an
SLE with <2. This lies outside the... Find in contentBookmark |
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