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Exceptional planes of percolation. (English) Zbl 0910.60076
Summary: Consider the standard continuous percolation in \(\mathbb{R}^4\), and choose the parameters so that the induced percolation on a fixed two-dimensional linear subspace is critical. Although two-dimensional critical percolation dies, we show that there are exceptional two-dimensional linear subspaces, in which percolation occurs.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
82C43 Time-dependent percolation in statistical mechanics
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