Generalized step-reinforced random walks on groups admit transition probability upper bounds determined by the isoperimetric profile of the Cayley graph, proving transience in Euclidean space for dimensions d≥3 and any reinforcement α<1, and resolving exponential decay for the elephant random walk.
Lalley.Random walks on infinite groups, volume 297 ofGraduate Texts in Mathematics
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Transition probabilities of step-reinforced random walks
Generalized step-reinforced random walks on groups admit transition probability upper bounds determined by the isoperimetric profile of the Cayley graph, proving transience in Euclidean space for dimensions d≥3 and any reinforcement α<1, and resolving exponential decay for the elephant random walk.