Communications in Mathematical Physics

, Volume 109, Issue 1, pp 109–156 | Cite as

Scaling relations for 2D-percolation

  • Harry Kesten


We prove that the relations 2D-percolation hold for the usual critical exponents for 2D-percolation, provided the exponents δ andv exist. Even without the last assumption various relations (inequalities) are obtained for the singular behavior near the critical point of the correlation length, the percolation probability, and the average cluster size. We show that in our models the above critical exponents have the same value for approach ofp to the critical probability from above and from below.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Cluster Size 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Harry Kesten
    • 1
  1. 1.Department of MathematicsCornell UniversityIthacaUSA

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