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Communications in Mathematical Physics

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

Scaling relations for 2D-percolation

  • Harry Kesten
Article

Abstract

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.

Keywords

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

© Springer-Verlag 1987

Authors and Affiliations

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

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