Critical Percolation: the Expected Number of Clusters in a Rectangle

Clément Hongler, Stanislav Smirnov
2011
Journal paper

Abstract

We show that for critical site percolation on the triangular lattice two new observables have conformally invariant scaling limits. In par- ticular the expected number of clusters separating two pairs of points converges to an explicit conformal invariant. Our proof is independent of earlier results and SLE techniques, and in principle should provide a new approach to establishing conformal invariance of percolation

Official source

https://infoscience.epfl.ch/record/200294?ln=en

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Critical values in an anisotropic percolation on $\mathbb{Z}^2$

Hao Xue

In this thesis, we consider an anisotropic finite-range bond percolation model on

\mathbb{Z}^2

. On each horizontal layer

\{(x,i):x\in\mathbb{Z}\}

for

i\in\mathbb{Z}

, we have edges

\langle(x,i),(y,i)\rangle

for

1\leq|x-y|\leq N

with $N\in\mathbb{N ...

EPFL2021

Critical Percolation: the Expected Number of Clusters in a Rectangle

THE PHASE TRANSITION FOR PLANAR GAUSSIAN PERCOLATION MODELS WITHOUT FKG

Critical values in an anisotropic percolation on $\mathbb{Z}^2$

Simulating Infiltration as a Sequence of Pinning and De-pinning Processes

THE PHASE TRANSITION FOR PLANAR GAUSSIAN PERCOLATION MODELS WITHOUT FKG

Critical values in an anisotropic percolation on $\mathbb{Z}^2$

Simulating Infiltration as a Sequence of Pinning and De-pinning Processes