Scaling Limits of Two-Dimensional Percolation: an Overview

TL;DR

This paper reviews recent advances in understanding the scaling limits of two-dimensional percolation, including convergence to Cardy's formula, SLE(6), and critical cluster boundaries.

Contribution

It provides an overview of the latest results on the convergence of percolation models to conformally invariant limits in two dimensions.

Findings

Convergence of crossing probabilities to Cardy's formula

Critical exploration paths to chordal SLE(6)

Full scaling limit of critical cluster boundaries

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.