Gamma-convergence of graph Ginzburg-Landau functionals

Yves van Gennip; Andrea L. Bertozzi

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arXiv · 1204.5220

Gamma-convergence of graph Ginzburg-Landau functionals

Yves van Gennip·Andrea L. Bertozzi

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Abstract

We study Gamma-convergence of graph based Ginzburg-Landau functionals, both the limit for zero diffusive interface parameter epsilon->0 and the limit for infinite nodes in the graph m -> infinity. For general graphs we prove that in the limit epsilon -> 0 the graph cut objective function is recovered. We show that the continuum limit of this objective function on 4-regular graphs is related to the total variation seminorm and compare it with the limit of the discretized Ginzburg-Landau functional. For both functionals we also study the simultaneous limit epsilon -> 0 and m -> infinity, by expressing epsilon as a power of m and taking m -> infinity. Finally we investigate the continuum limit for a nonlocal means type functional on a completely connected graph.

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BibTeX RIS

Yves van Gennip, Andrea L. Bertozzi. 2012-04-23. Gamma-convergence of graph Ginzburg-Landau functionals. https://arxiv.org/abs/1204.5220

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