Self-avoiding walks and amenability

zbMath1376.05068arXiv1510.08659MaRDI QIDQ1684654

Zhongyang Li, Geoffrey R. Grimmett

Publication date: 12 December 2017

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.08659

zbMATH Keywords

Cayley graphspectral radiusharmonic functionunimodularityamenable groupself-avoiding walkGrigorchuk groupelementary amenable groupconnective constantBaumslag-Solitar groupHigman groupgraph height functiongroup height functionindicable groupspectral bottom

Mathematics Subject Classification ID

Geometric group theory (20F65) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Enumeration in graph theory (05C30) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items

Connective constants and height functions for Cayley graphs ⋮ Weighted self-avoiding walks ⋮ Self-Avoiding Walks and Connective Constants ⋮ A general bridge theorem for self-avoiding walks ⋮ Cubic graphs and the golden mean ⋮ Self-avoiding walk on nonunimodular transitive graphs ⋮ Locality of connective constants ⋮ Positive speed self-avoiding walks on graphs with more than one end ⋮ Locality of the critical probability for transitive graphs of exponential growth

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