Abstract
Schramm’s Locality Conjecture asserts that the value of the critical parameter of a graph satisfying depends only on its local structure. In this paper, we prove this conjecture in the particular case of transitive graphs with polynomial growth. Our proof relies on two recent works about such graphs, namely supercritical sharpness of percolation by the same authors and a finitary structure theorem by Tessera and Tointon.
Citation
Daniel Contreras. Sébastien Martineau. Vincent Tassion. "Locality of percolation for graphs with polynomial growth." Electron. Commun. Probab. 28 1 - 9, 2023. https://doi.org/10.1214/22-ECP508
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