Question: Markov chain (high-dimensional random walk, transience) Consider the simple random walk on the d-dimensional lattice S = Zd. Any state r E Zd has 2d

Markov chain

(high-dimensional random walk, transience) Consider the simple random walk on the d-dimensional lattice S = Zd. Any state r E Zd has 2d nearest neighbors denoted by M(x). The simple random walk is defined by the Markov transition P(I, y) = 2d 1N(x) (y) If d > 3, show that all states of the Markov chain defined above are transient

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