Metric and spectral triples for Dirichlet and resistance forms

DOI10.4171/JNCG/195zbMath1327.81236arXiv1309.5937MaRDI QIDQ2354786

Michael Hinz, Alexander Teplyaev, Daniel J. Kelleher

Publication date: 24 July 2015

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.5937

zbMATH Keywords

Dirac operatorDirichlet formspectral tripleintrinsic metricresistance formConnes distanceKusuoka measure

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Noncommutative differential geometry (46L87) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Dirichlet forms (31C25) Noncommutative geometry in quantum theory (81R60) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Measures on Boolean rings, measure algebras (28A60) Noncommutative geometry (à la Connes) (58B34) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

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Cites Work

• The construction of Brownian motion on the Sierpinski carpet
• Uniqueness of Brownian motion on Sierpiński carpets
• Localization at large disorder and at extreme energies: an elementary derivation
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets

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