Add to ORKGScherk's graph is a subgraph of the three-dimensional lattice. It was shown by Markvorsen, McGuinness and Thomassen (1992) that Scherk's graph is transient. Consider the Bernoulli bond percolation in Scherk's graph. We prove that the infinite cluster is transient for p > 1/2 and is recurrent for p < 1/2. This implies the well-known result of Grimmett, Kesten and Zhang (1993) on the transience of the infinite cluster of the Bernoulli bond percolation in the three-dimensional lattice for p > 1/2. On the other hand, Scherk's graph exhibits a new dichotomy in the supercritical region.Statistics & ProbabilitySCI(E)1ARTICLE4828-8403
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In 1993, Menshikov and Zuev introduced ρ−percolation model, in which a path of a graph is ρ−passable...
We study Bernoulli bond percolation on nonunimodular quasi-transitive graphs, and more generally gra...
Funder: University of CambridgeAbstract: Let G be a connected, locally finite, transitive graph, and...
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We study bond percolation evolving in time in such a way that the edges turn on and off independentl...
This thesis is an investigation of some aspects of inhomogeneous Bernoulli bond percolation in two d...
In dynamical percolation, the status of every bond is refreshed according to an independent Poisson ...
Abstract: We prove that Bernoulli bond percolation on any nonamenable, Gromov hyperbolic, quasi-tran...
Abstract. Two vertices x and y are said to be finitely connected if they belong to the same cluster ...
Hermon and Hutchcroft have recently proved the long-standing conjecture that in Bernoulli(p) bond pe...
We establish several equivalent characterisations of the anchored isoperimetric dimension of supercr...
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We consider an i.i.d. supercritical bond percolation on Z^d , every edge is open with a probability ...
In 1993, Menshikov and Zuev introduced ρ−percolation model, in which a path of a graph is ρ−passable...
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