Plot Markov chain eigenvalues

`eigplot(`

creates a plot containing the eigenvalues of the transition matrix of the discrete-time Markov chain `mc`

)`mc`

on the complex plane. The plot highlights the following:

Unit circle

Perron-Frobenius eigenvalue at (1,0)

Circle of second largest eigenvalue magnitude (SLEM)

Spectral gap between the two circles, which determines the mixing time

[1]
Gallager, R.G. *Stochastic Processes: Theory for Applications.* Cambridge, UK: Cambridge University Press, 2013.

[2]
Horn, R., and C. R.
Johnson. *Matrix Analysis.* Cambridge, UK: Cambridge University Press,
1985.

[3]
Seneta, E. *Non-negative Matrices and Markov Chains.* New York, NY: Springer-Verlag, 1981.