arXiv:0810.1002 Abstract | arXiv Analytics

arXiv:0810.1002 [math.PR]Abstract References Reviews Resources

Scaling Limits of Two-Dimensional Percolation: an Overview

Published 2008-10-06Version 1

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.

Comments: 16 pages, 1 figure; written for a special issue of Satistica Neerlandica dedicated to EURANDOM's tenth anniversary

Categories: math.PR, cond-mat.stat-mech, math-ph, math.MP

Subjects: 82B27, 60K35, 82B43, 60D05, 30C35

Keywords: two-dimensional percolation, percolation scaling limits, chordal sle, full scaling limit, cardys formula

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