Recurrence and Eigenfunction Methods for Non-Trivial Models of Discrete Binary Choice

نویسندگان

چکیده

Understanding how systems relax to equilibrium is a core theme of statistical physics, especially in economics, where are known be subject extrinsic noise not included simple agent-based models. In models binary choice—ones much more complicated than Kirman’s model ant recruitment—such relaxation dynamics become difficult determine analytically and require solving three-term recurrence relation the eigendecomposition stochastic process. this paper, we derive concise closed-form solution linear relation. Its has traditionally relied on cumbersome continued fractions, instead employ algebraic approach that leverages properties lower-triangular tridiagonal matrices express terms using finite set orthogonal polynomials. We pay special attention power series coefficients Heun functions, which also important fields such as quantum mechanics general relativity, well choice studied here. then apply find equations describing steady-state behavior social through eigendecomposition. This application showcases potential our an off-the-shelf previously been reported, allowing for easy identification eigenspectra one-dimensional, one-step, continuous-time Markov processes.

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ژورنال

عنوان ژورنال: Entropy

سال: 2023

ISSN: ['1099-4300']

DOI: https://doi.org/10.3390/e25070996