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On some generalized reinforced random walk on integers. (English) Zbl 1196.60054
Summary: We consider Reinforced Random Walks where transitions probabilities are a function of the proportions of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to R. Pemantle [Ann. Probab. 16, No. 3, 1229–1241 (1988; Zbl 0648.60077)] on trees

MSC:
60F20 Zero-one laws
60G50 Sums of independent random variables; random walks
60C05 Combinatorial probability
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