A Superdiffusive Local Limit Theorem for the Elephant Random Walk and the Breakdown of Log-Concavity

Hélio Trinas, Glauco Valle

Let $(S_n{)}_{n\ge 1}$ be the one-dimensional Elephant Random Walk (ERW) in the superdiffusive regime, with memory parameter $p\in (3/4,1)$ and first-step bias $\mathbb{P}(S_1=1)=q$.…