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, 
, 并且每个符号以 1/2 的概率独立且随机地选择。令人惊讶的是，Viswanath (2000) 证明了
的值都存在。临界值 
使得 
由下式给出
随机矩阵 的迭代乘法中 (Bougerol and Lacrois 1985, pp. 11 和 157)。