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- W2794718326 abstract "We answer a question of Benjamini and Schramm by proving that under reasonable conditions, quotienting a graph with $p_c<1$ strictly increases the value of $p_c$. More precisely, let $mathcal{G}=(V,E)$ be a quasi-transitive graph with $p_c(mathcal{G})<1$, and let $G$ be a nontrivial group that acts freely on $V$ by graph automorphisms. Assume that $mathcal{H}:=mathcal{G}/G$ is quasi-transitive. Then, one has $p_c(mathcal{G})<p_c(mathcal{H})$. We also investigate the same question beyond this setting: we explain why no condition in the above result can be removed, which more general result can though be obtained, and ask a question on quotients by non-free group actions. The proof makes use of a coupling built by lifting the exploration of the cluster, and an essential (exploratory) enhancement." @default.
- W2794718326 created "2018-04-06" @default.
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- W2794718326 date "2018-03-26" @default.
- W2794718326 modified "2023-10-16" @default.
- W2794718326 title "Strict monotonicity of $p_c$ under covering maps" @default.
- W2794718326 hasPublicationYear "2018" @default.
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