Elephant random walks on d-regular infinite trees have asymptotic speed (d-2)/d independent of memory parameter p, with p-dependent upper bounds on convergence rate that exhibit a phase transition at p_d = (d+1)/(2d).
Strong limit theorems for step-reinforced random walks
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Elephant random walks on infinite Cayley trees
Elephant random walks on d-regular infinite trees have asymptotic speed (d-2)/d independent of memory parameter p, with p-dependent upper bounds on convergence rate that exhibit a phase transition at p_d = (d+1)/(2d).