Eigenvalues and Eigenvectors of Tau Matrices with Applications to Markov Processes and Economics

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

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

Eigenvalues and eigenvectors

Tau matrices

Queuing models

Random walks

Diffusion processes

Wealth and income inequality

Portfolio dynamics

Publication and Content Type

ref (subject category)

art (subject category)