DIEGO ARMENTANO, GAUTAM CHINTA, SIDDHARTHA SAHI, MICHAEL SHUB
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引用次数: 0
Abstract
We consider orthogonally invariant probability measures on $\operatorname {\mathrm {GL}}_n(\mathbb {R})$ and compare the mean of the logs of the moduli of eigenvalues of the matrices with the Lyapunov exponents of random matrix products independently drawn with respect to the measure. We give a lower bound for the former in terms of the latter. The results are motivated by Dedieu and Shub [On random and mean exponents for unitarily invariant probability measures on $\operatorname {\mathrm {GL}}_n(\mathbb {C})$. Astérisque287 (2003), xvii, 1–18]. A novel feature of our treatment is the use of the theory of spherical polynomials in the proof of our main result.
我们考虑了$\operatorname {\mathrm {GL}}_n(\mathbb {R})$上的正交不变概率度量，并比较了矩阵特征值对数的均值与随机矩阵乘积的李雅普诺夫指数，随机矩阵乘积是相对于度量独立抽取的。我们用后者给出了前者的下限。这些结果来自 Dedieu 和 Shub [On random and mean exponents for unitarily invariant probability measures on $\operatorname {\mathrm {GL}}_n(\mathbb {C})$.Astérisque 287 (2003), xvii, 1-18].我们的处理方法的一个新特点是在证明我们的主要结果时使用了球面多项式理论。
$\operatorname {\mathrm {GL}}_n(\mathbb {R})$ and compare the mean of the logs of the moduli of eigenvalues of the matrices with the Lyapunov exponents of random matrix products independently drawn with respect to the measure. We give a lower bound for the former in terms of the latter. The results are motivated by Dedieu and Shub [On random and mean exponents for unitarily invariant probability measures on 
$\operatorname {\mathrm {GL}}_n(\mathbb {C})$. Astérisque 287 (2003), xvii, 1–18]. A novel feature of our treatment is the use of the theory of spherical polynomials in the proof of our main result.
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