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- W220092022 abstract "The connective constant $mu(G)$ of a quasi-transitive graph $G$ is the exponential growth rate of the number of self-avoiding walks from a given origin. We prove a locality theorem for connective constants, namely, that the connective constants of two graphs are close in value whenever the graphs agree on a large ball around the origin (and a further condition is satisfied). The proof exploits a generalized bridge decomposition of self-avoiding walks, which is valid subject to the assumption that the underlying graph is quasi-transitive and possesses a so-called graph height function. It is proved that a broad category of transitive graphs have graph height functions." @default.
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- W220092022 date "2014-11-29" @default.
- W220092022 modified "2023-09-27" @default.
- W220092022 title "Locality of connective constants, I. Transitive graphs" @default.
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