随机矩阵与广义量子点散射体的乘积
Products of random matrices and generalised quantum point scatterers
摘要：
对于每一个$2\times2$矩阵的乘积，都对应一个一维薛定谔方程，其势由广义点散射体组成。{ \em random}矩阵的乘积是通过使这些相互作用及其位置随机而获得的。我们展示了一个简单的一维量子模型，对应于$\text{SL}(2, {\mathbb R})$中最一般的矩阵乘积。我们使用这种对应关系找到新的例子，产品的随机矩阵的不变测度可以表示在简单的分析。
英文摘要：
To every product of $2\times2$ matrices, there corresponds a one-dimensional Schrödinger equation whose potential consists of generalised point scatterers. Products of {\em random} matrices are obtained by making these interactions and their positions random. We exhibit a simple one-dimensional quantum model corresponding to the most general product of matrices in $\text{SL}(2, {\mathbb R})$. We use this correspondence to find new examples of products of random matrices for which the invariant measure can be expressed in simple analytical terms.
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