343.Ant on a Cube
★★★markov chainsCh. 6 — Random Variables and Expectation444+ Problems in Probability
An ant stands on a vertex of a cube and at each step moves to one of the three adjacent vertices with equal probability. Find the expected number of steps for the ant to return to its starting vertex.
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For a random walk on a regular graph, the stationary distribution is uniform — and expected return time is .
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