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Uniqueness in two-dimensional rigidity percolation
Published online by Cambridge University Press: 06 March 2001
Abstract
For bond percolation on the two-dimensional triangular lattice with arbitrary retention parameter p ∈ [0, 1], we show that the number of infinite rigid components is a.s. at most 1. This proves a conjecture by Holroyd. Further results, concerning simultaneous uniqueness, and continuity (in p) of the probability that a given edge is in an infinite rigid component, are also obtained.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 130 , Issue 1 , January 2001 , pp. 175 - 188
- Copyright
- 2001 Cambridge Philosophical Society
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