Scaling Limits of Two-Dimensional Percolation: an Overview

2008/10/06 by Camia, Federico
#30C35 #60D05 #60K35 #82B27 #82B43 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.0810.1002

Abstract

We present a review of the recent progress on percolation scaling limits in two dimensions. In particular, we will consider the convergence of critical crossing probabilities to Cardy's formula and of the critical exploration path to chordal SLE(6), the full scaling limit of critical cluster boundaries, and near-critical scaling limits.

Related

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• The Full Scaling Limit of Two-Dimensional Critical Percolation
• Two-Dimensional Scaling Limits via Marked Nonsimple Loops
• The scaling limit of the incipient infinite cluster in high-dimensional percolation. I. Critical exponents
• Restricted percolation critical exponents in high dimensions