On the scaling limits of planar percolation

TL;DR

This paper proves that all scaling limits of critical planar percolation are black noise, confirming Tsirelson's conjecture, and applies to various models including site and bond percolation.

Contribution

It establishes the universality of the black noise scaling limit for critical planar percolation models and proposes a natural construction for these limits.

Findings

All scaling limits of critical planar percolation are black noise.

The results apply to site percolation on the triangular grid and bond percolation on the square grid.

A natural construction for the scaling limit of planar percolation is suggested.

Abstract

We prove Tsirelson's conjecture that any scaling limit of the critical planar percolation is a black noise. Our theorems apply to a number of percolation models, including site percolation on the triangular grid and any subsequential scaling limit of bond percolation on the square grid. We also suggest a natural construction for the scaling limit of planar percolation, and more generally of any discrete planar model describing connectivity properties.