论文标题
tau矩阵的特征值和特征向量，以及马尔可夫流程和经济学的应用
Eigenvalues and Eigenvectors of Tau Matrices with Applications to Markov Processes and Economics
论文作者
论文摘要
在矩阵位移分解的上下文中，Bozzo和di fiore引入了所谓的$τ_ {\ varepsilon，φ} $ algebra，这是Bini和Capovani最初提出的较知名$τ$ algebra的概括。我们研究了$τ_ {\ varepsilon，φ} $代数的发电机$ t_ {n，\ varepsilon，φ} $的特征值和特征向量的属性。特别是，我们得出了$ t_ {n，\ varepsilon，φ} $和相关特征向量的异常值的渐近学；我们获得了$ t_ {n，\ varepsilon，φ} $的特征值的方程式，该方程也提供了$ t_ {n，\ varepsilon，φ} $的特征向量;然后，我们计算$ t_ {n，\ varepsilon，φ} $的完整特征组成，在特定情况下$ \varepsilonφ= 1 $。我们还在排队模型，随机步行和扩散过程的背景下提出了结果的应用，并特别注意了它们在财富/收入不平等和投资组合动态的研究中的影响。
In the context of matrix displacement decomposition, Bozzo and Di Fiore introduced the so-called $τ_{\varepsilon,φ}$ algebra, a generalization of the more known $τ$ algebra originally proposed by Bini and Capovani. We study the properties of eigenvalues and eigenvectors of the generator $T_{n,\varepsilon,φ}$ of the $τ_{\varepsilon,φ}$ algebra. In particular, we derive the asymptotics for the outliers of $T_{n,\varepsilon,φ}$ and the associated eigenvectors; we obtain equations for the eigenvalues of $T_{n,\varepsilon,φ}$, which provide also the eigenvectors of $T_{n,\varepsilon,φ}$; and we compute the full eigendecomposition of $T_{n,\varepsilon,φ}$ in the specific case $\varepsilonφ=1$. We also present applications of our results in the context of queuing models, random walks, and diffusion processes, with a special attention to their implications in the study of wealth/income inequality and portfolio dynamics.
