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math.PR2026
Limit theorems for amnesic elephant Random walks with random increment sizes
Cristian F. Coletti, Rafael Souza Dos Santos, Glauco Valle
We introduce a generalized amnesic elephant random walk in which, at each time, the direction of an underlying amnesic elephant random walk selects one of two increment distributio…
math.PR2026
A Superdiffusive Local Limit Theorem for the Elephant Random Walk and the Breakdown of Log-Concavity
Hélio Trinas, Glauco Valle
Let be the one-dimensional Elephant Random Walk (ERW) in the superdiffusive regime, with memory parameter and first-step bias .…