For random metastable interval maps, the small-perturbation jump times and destinations converge to an averaged continuous-time Markov chain, and the quenched diffusion coefficient equals an explicit formula in that chain's generator.
Dynamical spectrum via determinant-free linear algebra
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We consider a sequence of matrices that are associated to Markov dynamical systems and use determinant-free linear algebra techniques (as well as some algebra and complex analysis) to rigorously estimate the eigenvalues of every matrix simultaneously without doing any calculations on the matrices themselves. As a corollary, we obtain mixing rates for every system at once, as well as symmetry properties of densities associated to the system; we also find the spectral properties of a sequence of related factor systems.
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Jumping for diffusion in random metastable systems
For random metastable interval maps, the small-perturbation jump times and destinations converge to an averaged continuous-time Markov chain, and the quenched diffusion coefficient equals an explicit formula in that chain's generator.