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].
For the entire collection see [Zbl 0930.00053].
Reviewer: Ove Frank (Stockholm)
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 |