In the Tree Builder Random Walk, odd growth periods force ballistic transience, while even growth periods yield null recurrence under slow-growth environments and trapping under fast-growth environments.
Davis: Reinforced Random Walk, Probability Theory and Related Fields, 84(2), 203-229, (1990)
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Tree Builder Random Walk: recurrence, transience and ballisticity
In the Tree Builder Random Walk, odd growth periods force ballistic transience, while even growth periods yield null recurrence under slow-growth environments and trapping under fast-growth environments.