@inproceedings{ProblemS1, title={Problem Set 1 Solutions}, author={} }

1. If G = (V, E) is bipartite, with bipartition V = V 1 ∪ V 2 , then it is obvious that the random walk is periodic: if the walk starts in V 1 then any state in V 1 can be visited only at even time steps. For the converse, we will show that if G is not bipartite then the random walk is aperiodic. So suppose G is not bipartite; then it contains a cycle of… CONTINUE READING

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