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Background (potential theory and ergodic theory) 303 2. Problems: Solvable groups and exponential growth groups 304 3. Nilpotent covers of compact manifolds (Theorem 1) 305 4. -nilpotent covers of recurrent manifolds (Theorem 2) 309 5. A natural projection of bounded functions on to bounded harmonic functions (Theorem 3) 310 6. The Kelvin-Nevanlinna-Royden recurrence criterion (Theorems 4, 4') 312 7. Discretization of the random motion in the *-recurrent case (Theorem 5) 315 8. Discretization of the random motion in the cocompact case (Theorem 6) 318
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Lyons et al. (1984) studied this question.
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