Locality of percolation for graphs with polynomial growth
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Date
2023
Publication Type
Journal Article
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Abstract
Schramm's Locality Conjecture asserts that the value of the critical parameter pc of a graph satisfying pc < 1 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.
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published
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Journal / series
Volume
28
Pages / Article No.
1
Publisher
Institute of Mathematical Statistics
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Subject
percolation; Schramm's Locality Conjecture; transitive graphs of polynomial growth
Organisational unit
09584 - Tassion, Vincent / Tassion, Vincent
Notes
Funding
851565 - Critical and supercritical percolation (EC)