=+31. A simple change of Ehrenfests Markov chain in Example 7.3.3 renders it ergodic. At each step

Question:

=+31. A simple change of Ehrenfest’s Markov chain in Example 7.3.3 renders it ergodic. At each step of the chain, flip a fair coin. If the coin lands heads, switch the chosen molecule to the other half of the box. If the coin lands tails, leave it where it is. Show that Ehrenfest’s chain with holding is ergodic and converges to the binomial distribution π with m trials and success probability 1

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