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Uniqueness of infinite rigid components in percolation models: the case of nonplanar lattices

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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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Correspondence to Olle Häggström.

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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).

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  • Euclidean Space
  • Periodic Lattice
  • Percolation Model
  • Planar Setting
  • Bond Percolation