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- W2296946504 abstract "For a transitive infinite connected graph $G$, let $mu(G)$ be its connective constant. Denote by $mathbf{cal G}$ the set of Cayley graphs for finitely generated infinite groups with an infinite-order generator which is independent of other generators. Assume $Ginmathbf{cal G}$ is a Cayley graph of a finitely presented group, and Cayley graph sequence ${G_n}_{n=1}^{infty}subset mathbf{cal G}$ converges locally to $G.$ Then $mu(G_n)$ converges to $mu(G)$ as $nrightarrowinfty.$ This confirms partially a conjecture raised by Benjamini [2013. {it Coarse geometry and randomness.} Lect. Notes Math. {bf 2100}. Springer.] that connective constant is continuous with respect to local convergence of infinite transitive connected graphs." @default.
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- W2296946504 date "2014-10-08" @default.
- W2296946504 modified "2023-09-24" @default.
- W2296946504 title "Connective Constants on Cayley Graphs" @default.
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- W2296946504 doi "https://doi.org/10.48550/arxiv.1410.2591" @default.
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