论文标题
通过无决定性线性代数的动力频谱
Dynamical spectrum via determinant-free linear algebra
论文作者
论文摘要
我们考虑一系列与马尔可夫动力学系统相关的矩阵，并使用无决定性的线性代数技术（以及一些代数和复杂分析），以严格估计每个矩阵的特征值，而无需对矩阵本身进行任何计算。作为推论，我们立即获得每个系统的混合速率，以及与系统相关的密度的对称性。我们还找到了一系列相关因子系统的光谱特性。
We consider a sequence of matrices that are associated to Markov dynamical systems and use determinant-free linear algebra techniques (as well as some algebra and complex analysis) to rigorously estimate the eigenvalues of every matrix simultaneously without doing any calculations on the matrices themselves. As a corollary, we obtain mixing rates for every system at once, as well as symmetry properties of densities associated to the system; we also find the spectral properties of a sequence of related factor systems.
