Asymptotic Analysis of the Ginzburg-Landau Functional on Point Clouds

Matthew Thorpe, Florian Theil

Research output: Contribution to journalArticlepeer-review


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 Ψ_n 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.
Original languageEnglish
Pages (from-to)387-427
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Issue number2
Early online date27 Dec 2018
Publication statusPublished - 2019


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