If you never forgot a single step you ever took, you’d eventually start moving in a way that breaks the laws of physics.
March 30, 2026
Original Paper
Elephant Random Walks on Coverings of Dipole Graphs
arXiv · 2603.26059
The Takeaway
Most moving things in nature, like gas molecules or drifting dust, have no 'memory' of their path. By modeling a walker that refers to its entire history for every new step, researchers found a 'superdiffusive' movement style that behaves unlike any standard physical model.
From the abstract
In the present paper, we introduce and analyze elephant random walks (ERWs) on bipartite periodic lattices arising as coverings of dipole graphs. We focus on lattices whose admissible step directions in the two parts of the bipartition are negatives of each other and disjoint. On such graphs, we define an ERW in which each step is chosen by referring to the entire history of the walk. The ERW on the hexagonal lattice is a prototypical example of our model. The definition and asymptotic analysis