We prove uniqueness of the infinite rigid component for standard bond percolation on periodic lattices in d-dimensional Euclidean space for arbitrary d, and more generally when the lattice is a quasi-transitive and amenable graph. Our approach to uniqueness of the infinite rigid component improves earlier ones, that were confined to planar settings.
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Research supported by the Swedish Research Council
Mathematics Subject Classification (2000): 60K35, 82B43
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Häggström, O. Uniqueness of infinite rigid components in percolation models: the case of nonplanar lattices. Probab. Theory Relat. Fields 127, 513–534 (2003). https://doi.org/10.1007/s00440-003-0290-2
- Euclidean Space
- Periodic Lattice
- Percolation Model
- Planar Setting
- Bond Percolation