Let's think about the irreducibility and aperiodicity conditions of the Basic Limit Theorem as applied to the Metropolis

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Let S Think About The Irreducibility And Aperiodicity Conditions Of The Basic Limit Theorem As Applied To The Metropolis 1 (119.3 KiB) Viewed 73 times

Let's think about the irreducibility and aperiodicity conditions of the Basic Limit Theorem as applied to the Metropolis method. Suppose that the graph structure on S is a connected graph. Let a be any distribution other than Trw, the stationary distribution of a random walk on the graph. Show that the Basic Limit Theorem implies that the Metropolis chain converges in distribution to n.