Asymptotic analysis of the Ginzburg–Landau functional on point clouds

DOI10.1017/prm.2018.32zbMath1417.49013arXiv1604.04930OpenAlexW2963584757WikidataQ128692102 ScholiaQ128692102MaRDI QIDQ5383346

Matthew Thorpe, Florian Theil

Publication date: 21 June 2019

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.04930

zbMATH Keywords

phase transitionsGinzburg-Landau functional\(\Gamma\)-convergencePDEs on graphslarge data asymptoticstotal variation on graphs

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Methods involving semicontinuity and convergence; relaxation (49J45) Existence of optimal solutions to problems involving randomness (49J55)

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Cites Work

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• Continuum limit of total variation on point clouds
• The \(L^\infty\) optimal transport: infinite cyclical monotonicity and the existence of optimal transport maps
• An introduction to \(\Gamma\)-convergence
• The geometry of optimal transportation
• Relaxing the uniformity and independence assumptions using the concept of fractal dimension
• A nonlocal anisotropic model for phase transitions
• The gradient theory of phase transitions and the minimal interface criterion
• \(\Gamma\)-convergence of graph Ginzburg-Landau functionals
• A first-order primal-dual algorithm for convex problems with applications to imaging
• Mean curvature, threshold dynamics, and phase field theory on finite graphs
• Complex networks: structure and dynamics
• Consistency of Cheeger and Ratio Graph Cuts
• Variational Analysis in Sobolev andBVSpaces
• Scale-Free Networks
• Convergence of the $k$-Means Minimization Problem using $\Gamma$-Convergence
• On the Rate of Convergence of Empirical Measures in ∞-transportation Distance
• The $\infty$-Wasserstein Distance: Local Solutions and Existence of Optimal Transport Maps
• Random Geometric Graphs
• Diffuse Interface Models on Graphs for Classification of High Dimensional Data
• Community Detection Using Spectral Clustering on Sparse Geosocial Data
• Exploring complex networks