Eigenvalues and eigenvectors of tau matrices with applications to Markov processes and economics. (English) Zbl 1471.15004

Ekström, Sven-Erik; Garoni, Carlo; Jozefiak, Adam; Perla, Jesse

Linear Algebra Appl. 627, 41-71 (2021).

The authors study the spectral properties of the generator of a matrix algebra in the context of matrix displacement decompositions. They derive precise asymptotics for the outliers and the associated eigenvectors. Further, they obtain determining equations for the eigenvalues and eigenvectors, with a focus on the hyperbolic equations for the outlier eigenpairs. The full eigendecomposition is constructed in a particular case. Finally, they present applications to queuing models, random walks, diffusion processes, and economics, with a special emphasis on wealth/income inequality and portfolio dynamics.

Reviewer: George Stoica (Saint John)

MSC:

15A18	Eigenvalues, singular values, and eigenvectors
15A30	Algebraic systems of matrices
15B05	Toeplitz, Cauchy, and related matrices
60K25	Queueing theory (aspects of probability theory)
60G50	Sums of independent random variables; random walks
60J60	Diffusion processes
91G10	Portfolio theory

Keywords:

eigenvalues; eigenvectors; tau matrices; queuing models; random walks; diffusion processes; wealth and income inequality; portfolio dynamics

Software:

Julia

References:

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