英文稱作 percolation,拉丁字源:per 為穿透之意,cōlō 為流動之意,中文因此翻譯做「滲透」。
英文動詞 to percolate 在中文同樣翻譯做「滲透」,且在我們的模型中,常常代表「無窮大連通元件存在」的意思。
伯努力滲透模型是最容易定義的滲透模型,給定一個邊數為可數多個的圖,
(定義模型,簡單敘述並且描述重要結果,其他細解參考下面網址)
更多資訊請參考伯努力滲透模型。
¶ 隨機連通元件模型 (random-cluster model)
First consider a collection of random variables {wij}i,j∈N taking non-negative values.
Latter we assign an integer point (i,j) in the first quarter of Z2 a random variable wij.
For M,N∈N, define a up/right path π from (1,1) to (M,N) as following: π={t1,t2,...,tM+N−1∈Z2} satisfies t1=(1,1),tM+N−1=(M,N) and ti+1−ti∈{(1,0),(0,1)} for i∈{1,2,...,M+N−2}. Denote ΠM,N to be the set collecting all such up/right paths from (1,1) to (M,N).
Define the random variable L(M,N)=π∈ΠM,Nmax(i,j)∈π∑wij, which is called the last passage time from (1,1) to (M,N).
If we consider wij as the time when we need to pass the point (i,j), then L(M,N) can be thought as the maximum time we needed starting from (1,1) to (M,N).