高密度情形格点Sierpinski地毯上渗流模型无穷开串的唯一性

Uniqueness of the Infinite Open Cluster for High-Density Percolation on Lattice Sierpinski Carpet

本文证明高密度情形格点Ｓｉｅｒｐｉｎｓｋｉ地毯上边渗流模型无穷开串的唯一性，同时给出本模型相变存在性的一个新的证明．一种再标度技巧被发展并用作我们证明的主要工具．

We prove the uniqueness of infinite open cluster for high-density bond per- colation on lattice Sierpinski Carpet, forthermore, an alternative proof of the existence of phase transition of the model is given. A rescaling technique is developed and used as the main tool of our proofs.