Benjamini, Itai; Lyons, Russell; Schramm, Oded Percolation perturbations in potential theory and random walks. (English) Zbl 0958.05121 Picardello, Massimo (ed.) et al., Random walks and discrete potential theory. Cortona 1997. Proceedings of the conference, Cortona, Italy, June 1997. Cambridge: Cambridge University Press. Symp. Math. 39, 56-84 (1999). By Bernoulli selection of vertices or edges in a graph, a subgraph is obtained and its connected components are investigated. Percolation problems are examined by introducing a simple random walk on the subgraphs. The main result is that the connected components admit certain invariances with respect to the isoperimetric dimension of the graph.For the entire collection see [Zbl 0930.00053]. Reviewer: Ove Frank (Stockholm) Cited in 3 ReviewsCited in 26 Documents MSC: 05C80 Random graphs (graph-theoretic aspects) 82B43 Percolation 82C43 Time-dependent percolation in statistical mechanics 60K35 Interacting random processes; statistical mechanics type models; percolation theory Keywords:random percolation; automorphism group; invariant subgroups; isoperimetric dimension PDFBibTeX XMLCite \textit{I. Benjamini} et al., Symp. Math. 39, 56--84 (1999; Zbl 0958.05121) Full Text: arXiv