Locality of connective constants
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Grimmett, G., & Li, Z. (2018). Locality of connective constants. Discrete Mathematics, 341 (12), 3483-3497. https://doi.org/10.1016/j.disc.2018.08.013
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 unimodular graph height function.
External DOI: https://doi.org/10.1016/j.disc.2018.08.013
This record's URL: https://www.repository.cam.ac.uk/handle/1810/285046
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Licence URL: https://creativecommons.org/licenses/by-nc-nd/4.0/