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math.PR2024
On the limit law of the superdiffusive elephant random walk
Hélène Guérin, Lucile Laulin, Kilian Raschel +1
When the memory parameter of the elephant random walk is above a critical threshold, the process becomes superdiffusive and, once suitably normalised, converges to a non-Gaussian r…
math.PR2024
A universal scaling limit for diffusive amnesic step-reinforced random walks
Marco Bertenghi, Lucile Laulin
We introduce a variation of the step-reinforced random walk with general memory. For the diffusive regime, we establish a functional invariance principle and show that, given suita…