Uniform boundedness of critical crossing probabilities implies hyperscaling

C. Borgs, J. T. Chayes, H. Kesten, J. Spencer

Research output: Contribution to journalArticlepeer-review


We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1.

Original languageEnglish (US)
Pages (from-to)368-413
Number of pages46
JournalRandom Structures and Algorithms
Issue number3-4
StatePublished - 1999

ASJC Scopus subject areas

  • Software
  • General Mathematics
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics


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