Statistics Seminars: Hitting large sets
23 April 2012 14:00 in CM221
Given any irreducible discrete-time Markov chain on a finite state space, consider the largest expected hitting time $T(\alpha)$ of a set of stationary measure at least $\alpha$, $0 < \alpha < 1$. We describe tight relationships between $T(\alpha)$ and $T(\beta)$ for different choices of $\alpha$ and $\beta$. In particular, using an ergodic argument we show that, if $\alpha < 1/2$, then $T(\alpha) \leT(1/2)/\alpha$. A corollary is that, if the chain is reversible, $T(1/2)$ is equivalent to total variation mixing time of the chain, answering a question of Peres.
This is joint work with Simon Griffiths (IMPA), Roberto Oliveira (IMPA) and Viresh Patel (Durham).
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