The transition probabilities are given by the matrix [ pi_{1}=left{begin{array}{ccc} 0 & frac{1}{2} & frac{1}{2} frac{1}{2}
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The transition probabilities are given by the matrix
\[ \pi_{1}=\left\{\begin{array}{ccc} 0 & \frac{1}{2} & \frac{1}{2} \\ \frac{1}{2} & 0 & \frac{1}{2} \\ \frac{1}{2} & \frac{1}{2} & 0 \end{array}\right\} \]
Is Markov's ergodic theorem applicable in this case? If it is, then find the limiting probabilities.
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