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Percolation pp 169-185 | Cite as

Near the Critical Point: Rigorous Results

  • Geoffrey Grimmett

Abstract

It is the presence of circuits in L d which causes difficulties in exact calculations: there are many different paths joining two specified vertices, and pairs of such paths generally have edges in common In attempting to understand critical phenomena, it is usual to tackle first the corresponding problem on a rather special lattice, being a lattice which is devoid of circuits; we do this in the hope that the ensuing calculation will be simple but will help in the development of insight into more general situations. Such a lattice is called a tree, and it is to percolation on trees that this section is devoted.

Keywords

Critical Exponent Binary Tree Open Cluster Tauberian Theorem Critical Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

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Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • Geoffrey Grimmett
    • 1
  1. 1.School of MathematicsUniversity of BristolBristolEngland

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