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In and Out of Equilibrium 2Is Critical 2D Percolation Universal?

In and Out of Equilibrium 2: Is Critical 2D Percolation Universal? [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

In and Out of Equilibrium 2Is Critical 2D Percolation Universal?

Part of the Progress in Probability Book Series (volume 60)
Editors: Sidoravicius, Vladas; Vares, Maria Eulália
Beffara, Vincent
In and Out of Equilibrium 2 — Jan 1, 2008
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References (16)

Publisher
Birkhäuser Basel
Copyright
© Birkhäuser Basel 2008
ISBN
978-3-7643-8785-3
Pages
31 –58
DOI
10.1007/978-3-7643-8786-0_3
Publisher site
See Chapter on Publisher Site

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.]

Published: Jan 1, 2008

Keywords: Percolation; Conformal invariance; Complex structure; 82B43; 32G15; 82B27

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