Metric graphs, cross ratios, and Rayleigh's laws

DOI10.1216/rmj.2022.52.1403OpenAlexW2895705613WikidataQ114846375 ScholiaQ114846375MaRDI QIDQ2080685

Farbod Shokrieh, Robin de Jong

Publication date: 10 October 2022

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.02638

zbMATH Keywords

spanning treeLaplacianelectrical networkresistancecross ratiopotential kernelmetric graphenergy pairingRayleigh's law

Mathematics Subject Classification ID

Applications of graph theory (05C90) Small world graphs, complex networks (graph-theoretic aspects) (05C82) Combinatorial aspects of tropical varieties (14T15) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Analytic circuit theory (94C05) Distance in graphs (05C12)

Related Items (2)

Tropical moments of tropical Jacobians ⋮ Jumps in the height of the Ceresa cycle

Cites Work

• Metric properties of the tropical Abel-Jacobi map
• Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances
• Admissible pairing on a curve
• Random walks and the effective resistance of networks
• A new proof of R. Foster's averaging formula in networks
• Canonical measures on metric graphs and a Kazhdan's theorem
• Chip-firing games, potential theory on graphs, and spanning trees
• Uniform spanning forests
• The dissection of rectangles into squares
• Probability on Trees and Networks
• The capacity pairing.
• Algebraic Potential Theory on Graphs
• Harmonic Analysis on Metrized Graphs
• CANONICAL REPRESENTATIVES FOR DIVISOR CLASSES ON TROPICAL CURVES AND THE MATRIX–TREE THEOREM
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