Rahul Roy

A unidirectional elephant random walk with a power law memory

For the standard elephant random walk, Laulin (2022) studied the case when the increment of the random walk is not uniformly distributed over the past history and instead has a power law distribution.
We study such a problem for the unidirectional elephant random walk introduced by Harbola, Kumar and Lindenberg (2014).
Depending on the memory parameter $p$ and the power law exponent $\beta$, we obtain three distinct phases. In one such phase the elephant travels only a finite distance almost surely, the other phases are distinguished by the speed at which the elephant goes to infinity.

This work is based on two papers - ECP (2024) paper 78 and arXiv:2504.00566, both written jointly with Masato Takei (Yokohama National University) and Hideki Tanemura (Keio University).