Phase separation in random cluster models II: the droplet at equilibrium, and local deviation lower bounds
نویسنده
چکیده
We study the droplet that results from conditioning the planar subcritical Fortuin-Kasteleyn random cluster model on the presence of an open circuit Γ0 encircling the origin and enclosing an area of at least (or exactly) n . We consider local deviation of the droplet boundary, measured in a radial sense by the maximum local roughness, MLR ( Γ0 ) , this being the maximum distance from a point in the circuit Γ0 to the boundary ∂conv ( Γ0 ) of the circuit’s convex hull; and in a longitudinal sense by what we term maximum facet length, namely, the length of the longest line segment of which the polygon ∂conv (
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