Spectral purification in reversible Markov chains is controlled by a hidden parameter x_k driven by the eigenvalue ratio λ3/λ2, making six diagnostics equivalent and yielding non-asymptotic bounds on rigidity time plus a spectral entropy second law.
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Graph theory yields explicit combinatorial formulas showing mutual linearity for transient occupation probabilities and hitting time distributions in Markov networks.
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Spectral Purification in Reversible Markov Chains: Hidden Parameters, Observable Equivalence, and Finite-Time Rigidity
Spectral purification in reversible Markov chains is controlled by a hidden parameter x_k driven by the eigenvalue ratio λ3/λ2, making six diagnostics equivalent and yielding non-asymptotic bounds on rigidity time plus a spectral entropy second law.