Abstract
Let T be a locally finite, infinite tree. The simple random walk on T is the Markov chain in which transition from one vertex v to another vertex w occurs with probability 1/ d(v) (d(v) = degree of v ) if w is adjacent to v , and probability 0 otherwise. We study recurrence properties (no infinite tree is positive recurrent) and relations between the simple random walk and the tree structure, e.g. R -recurrence and R -transience, the action of a random walk on the branches and ends, the growth of a tree.
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