Communications in Mathematical Physics

, Volume 109, Issue 1, pp 109–156

Scaling relations for 2D-percolation

  • Harry Kesten

DOI: 10.1007/BF01205674

Cite this article as:
Kesten, H. Commun.Math. Phys. (1987) 109: 109. doi:10.1007/BF01205674


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.

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

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