In and Out of Equilibrium 2 pp 31-58

Part of the Progress in Probability book series (PRPR, volume 60)

Is Critical 2D Percolation Universal?

  • Vincent Beffara

Abstract

The aim of these notes is to explore possible ways of extending Smirnov’s proof of Cardy’s formula for critical site-percolation on the triangular lattice to other cases (such as bond-percolation on the square lattice); the main question we address is that of the choice of the lattice embedding into the plane which gives rise to conformal invariance in the scaling limit. Even though we were not able to produce a complete proof, we believe that the ideas presented here go in the right direction.

Keywords

Percolation Conformal invariance Complex structure 

Mathematics Subject Classification (2000)

82B43 32G15 82B27 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Vincent Beffara
    • 1
  1. 1.CNRS-UMPAEcole normale supérieure de LyonLyon cedex 07France

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