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).
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1 Pith paper cite this work. Polarity classification is still indexing.
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In a recent paper [2] the author introduced and investigated a random walk model similar to a model introduced in [1]. In these models the increment of the random walk depends on the complete past of the process. In this note I will point out that the models considered in [1] and [2] can be mapped onto each other one to one. They can be defined on a common probability space and hence all expectation values of the model [2] with parameter p are equal to the ones of [1] with a corresponding parameter $\tilde{p}$.
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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).