In this note we study the geometry of the largest component C1mathcal {C}_{1} of critical percolation on a finite graph G which satisfies the finite triangle condition, defined by Borgs et al. (Random Struct. Algorithms 27:137–184, 2005). There it is shown that this component is of size n 2/3, and here we show that its diameter is n 1/3 and that the simple random walk takes n steps to mix on it. By Borgs et al. (Ann. Probab. 33:1886–1944, 2005), our results apply to critical percolation on several high-dimensional finite graphs such as the finite torus mathbbZndmathbb{Z}_{n}^{d} (with d large and n→∞) and the Hamming cube {0,1} n .
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机译：在本说明中，我们研究了满足Borgs等人定义的有限三角形条件的有限图G上临界渗流的最大成分C 1 数学{C} _ {1}的几何形状。 （Random Struct。Algorithms 27：137–184，2005）。那里表明这个分量的大小为n 2/3 ，这里我们表明它的直径为n 1/3 ，简单的随机游走需要n步混合在一起。由博格斯等。 （Ann。Probab。33：1886-1944，2005），我们的结果适用于几个高维有限图上的临界渗流，例如有限圆环mathbbZ n n d mathbb {Z} _ {n} ^ {d}（具有d大且n→∞）和汉明立方体{0,1} n 。
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