Question: 13. Show that the symmetric random walk on the integer points Zd = (i1, i2, . . . , id ) : i j

13. Show that the symmetric random walk on the integer points Zd =



(i1, i2, . . . , id ) : i j = . . . ,−1, 0, 1, . . . , j = 1, 2, . . . , d


is recurrent if d = 1, 2 and transient if d ≥ 3. You should use the results of Problems 10.5.8 and 10.5.12, and you need do no more calculations.

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