Reversible Markov chains possess finite-time spectral rigidity controlled by eigenvalue separation, with two-sided bounds on rigidity time and a covariance-based spectral entropy theory.
Saad,Iterative Methods for Sparse Linear Systems, 2nd edition, SIAM, 2003
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Quantitative Spectral Rigidity and Finite-Time Spectral Thermodynamics in Reversible Markov Chains
Reversible Markov chains possess finite-time spectral rigidity controlled by eigenvalue separation, with two-sided bounds on rigidity time and a covariance-based spectral entropy theory.