Mean-field critical behaviour for correlation length for percolation in high dimensions

  title={Mean-field critical behaviour for correlation length for percolation in high dimensions},
  author={T. Hara},
  journal={Probability Theory and Related Fields},
  • T. Hara
  • Published 1990
  • Mathematics
  • Probability Theory and Related Fields
SummaryExtending the method of [27], we prove that the corrlation length ξ of independent bond percolation models exhibits mean-field type critical behaviour (i.e. ξ(p∼(pc−p)−1/2 asp↗pc) in two situations: i) for nearest-neighbour independent bond percolation models on ad-dimensional hypercubic lattice ℤd, withd sufficiently large, and ii) for a class of “spread-out” independent bond percolation models, which are believed to belong to the same universality class as the nearest-neighbour model… Expand
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