abstract:

We prove that the spectral radius of an i.i.d. random walk on ${\rm GL}_d(\Bbb{C})$ satisfies a strong law of large numbers under finite second moment assumption and a weak law of large numbers under finite first moment. No irreducibility assumption is supposed.

中文翻译：

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随机矩阵乘积谱半径的大数定律

摘要：

我们证明 ${\rm GL}_d(\Bbb{C})$ 上的 iid 随机游走的谱半径满足有限二阶矩假设下的强大数定律和有限一阶矩下的弱大数定律. 没有不可约假设。