Uniqueness in Two-dimensional Rigidity Percolation

  title={Uniqueness in Two-dimensional Rigidity Percolation},
  author={Olle Hh and A Om},
  • Olle Hh, A Om
  • Published 1999
For bond percolation on the two-dimensional triangular lattice with arbitrary retention parameter p 2 0; 1], we show that the number of innnite rigid components is a.s. at most one. 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 innnite rigid component, are also obtained. 

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