Eigenvalues of non-reversible Markov chains: their connection to mixing times, reversible Markov chains, and Cheeger inequalities
نویسنده
چکیده
We show a lower bound on mixing time for a non-reversible Markov chain in terms of its eigenvalues. This is used to show a bound on the real part of the complex-valued eigenvalues in terms of the realvalued eigenvalues of a related reversible chain, and likewise to bound the second largest magnitude eigenvalue. A myriad of Cheeger-like inequalities also follow for non-reversible chains, which even in the reversible case sharpen previously known results. The same argument also produces a new Cheeger-like inequality for the smallest eigenvalue of a reversible chain, and a Cheeger-like inequality for the second largest magnitude eigenvalue of a non-reversible chain.
منابع مشابه
Generalized Cheeger inequalities for eigenvalues of non-reversible Markov chains
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