Elsevier

Linear Algebra and its Applications

Volume 627, 15 October 2021, Pages 41-71
Linear Algebra and its Applications

Eigenvalues and eigenvectors of tau matrices with applications to Markov processes and economics

https://doi.org/10.1016/j.laa.2021.06.005Get rights and content
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Abstract

In the context of matrix displacement decomposition, Bozzo and Di Fiore introduced the so-called τε,φ algebra, a generalization of the well known τ algebra. We study the properties of eigenvalues and eigenvectors of the generator Tn,ε,φ of the τε,φ algebra. In particular, we derive the asymptotics for the outliers of Tn,ε,φ and the associated eigenvectors; we obtain equations for the eigenvalues of Tn,ε,φ, which provide also the eigenvectors of Tn,ε,φ; and we compute the full eigendecomposition of Tn,ε,φ in the specific case εφ=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.

MSC

15A18
15B05
60K25
60G50
60J60
91G10

Keywords

Eigenvalues and eigenvectors
Tau matrices
Queuing models
Random walks
Diffusion processes
Wealth and income inequality
Portfolio dynamics

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