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Regular Expansion for the Characteristic Exponent of a Product of 2 × 2 Random Matrices
Mathematical Physics, Analysis and Geometry ( IF 1 ) Pub Date : 2019-05-14 , DOI: 10.1007/s11040-019-9312-x
Benjamin Havret

We consider a product of 2 × 2 random matrices which appears in the physics literature in the analysis of some 1D disordered models. These matrices depend on a parameter 𝜖 > 0 and on a positive random variable Z. Derrida and Hilhorst (J. Phys. 16(12), 2641, 1983, § 3) conjecture that the corresponding characteristic exponent has a regular expansion with respect to 𝜖 up to — and not further — an order determined by the distribution of Z. We give a rigorous proof of that statement. We also study the singular term which breaks that expansion.

中文翻译:

2 × 2 随机矩阵乘积的特征指数的正则展开式

我们在分析一些一维无序模型时考虑物理文献中出现的 2 × 2 随机矩阵的乘积。这些矩阵取决于参数 𝜖 > 0 和正随机变量 Z. Derrida 和 Hilhorst (J. Phys. 16(12), 2641, 1983, § 3) 猜想相应的特征指数相对于𝜖 直到 - 而不是进一步 - 由 Z 的分布确定的顺序。我们给出了该陈述的严格证明。我们还研究了打破这种扩展的单数术语。
更新日期:2019-05-14
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