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Results tagged with mixing
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user 106074
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Must this upper bound on mixing time depend on the minimum stationary probability?
It is known fact that for a finite-state, reversible and ergodic Markov chain with transition matrix $M$, the following control on the mixing time holds
$$\left( \frac{1}{\gamma_\star - 1}\right)\ln{2 … } \leq t_{mix} \leq \frac{\ln(4/\pi_\star)}{\gamma_\star}$$
where $\pi$ is the stationary distribution $\pi M = \pi$,
$$\pi_\star = \min_i \pi(i),$$
the mixing time is defined by
$$t_{mix} = \min \{t …
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