Gradient models and kappa-harmonic functions

Abstract: This is joint work with Istvan Prause. We discuss random height models h:R^2 -> R and their associated limit shapes. A gradient model is one whose surface tension only depends on slope. Examples include the 6- and 8-vertex model and FK-percolation models, among many others. We show that limit shapes for such a model can be explicitly parameterized using kappa-harmonic functions, that is, solutions to the laplacian equation with spatially varying conductance kappa=kappa(x,y). Here kappa is the square root of the Hessian determinant of the surface tension.

mathematical physicsprobability

Audience: researchers in the topic

Probability and the City Seminar

Series comments: The Probability and the City Seminar is organized jointly by the probability groups of Columbia University and New York University.

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