The Scaling Limit of (Near-)Critical 2D Percolation

Abstract

The geometric analysis of the continuum scaling limit of two-dimensional critical percolation has made tremendous progress in recent years. In this extended abstract, we give a brief introduction to scaling limits and summarize some of the recent progress in percolation. We discuss in particular how to obtain the scaling limit of the collection of all macroscopic cluster boundaries, and how one can attempt to use it to understand and study the scaling limit of percolation “near” the critical point.