The Number of Incipient Spanning Clusters in Two-Dimensional Percolation

TL;DR

This paper uses conformal field theory to conjecture an exact probability formula for the number of spanning clusters in large 2D percolation systems, providing insights into their geometric properties.

Contribution

It introduces a conjectured exact expression for the probability of n spanning clusters in large rectangles or cylinders in 2D percolation.

Findings

Proposes an exact probability formula for spanning clusters

Utilizes conformal field theory methods

Enhances understanding of percolation cluster geometry

Abstract

Using methods of conformal field theory, we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k, in the limit when k is large.