The Incipient Infinite Cluster of the Uniform Infinite Half-Planar Triangulation

摘要

We introduce the Incipient Infinite Cluster (IIC) in the critical Bernoullisite percolation model on the Uniform Infinite Half-Planar Triangulation(UIHPT), which is the local limit of large random triangulations with aboundary. The IIC is defined from the UIHPT by conditioning the openpercolation cluster of the origin to be infinite. We prove that the IIC can beobtained by adding within the UIHPT an infinite triangulation with a boundarywhose distribution is explicit.