The Elephant Random Walk (ERW), introduced by Schütz and
Trimper (2004), has gained a lot of attention in recent years. We
consider a memory-based variation of the classical ERW. The aim is to
understand how much memory is 'enough' to observe an ERW-like behaviour.
In our model, we partition the memory into two subsets, $D_n$ and
$D_n^c$, such that the elephant behaves like the classical ERW model
when a step is chosen from $D_n^c$ and behaves differently when it is
chosen from $D_n$. We illustrate that in order to obtain a phase
transition, the size of $D_n^c$ needs to be more than half the entire
memory. This is joint work with Neeraja Sahasrabudhe (IISER Mohali) and
Debleena Thacker (Durham University).