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Asymptotic analysis of the Ginzburg–Landau functional on point clouds

  • Matthew Thorpe (a1) and Florian Theil (a1)


The Ginzburg–Landau functional is a phase transition model which is suitable for classification type problems. We study the asymptotics of a sequence of Ginzburg–Landau functionals with anisotropic interaction potentials on point clouds Ψn where n denotes the number data points. In particular, we show the limiting problem, in the sense of Γ-convergence, is related to the total variation norm restricted to functions taking binary values, which can be understood as a surface energy. We generalize the result known for isotropic interaction potentials to the anisotropic case and add a result concerning the rate of convergence.



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Present address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, email:



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