Elephants Explore in Spirals Sometimes
Abstract
Abstract We consider in this article an elephant random walk evolving in the plane. Specifically, this is a reinforced stochastic process in which the đť‘›th step is given by a random rotation of one of the previous steps chosen uniformly at random. We obtain a central limit theorem for this process, which shows that the process follows a randomly rotated logarithmic spiral at large times, with Gaussian fluctuations.
Fields of Study & Subjects
Diffusion and Search Dynamics
Stochastic processes and statistical mechanics
Random Matrices and Applications
Publication details
- Journal / source
- Stochastics and Quality Control
- Publisher
- Walter de Gruyter GmbH
- Publication date
- 5 June 2026
- Language
- EN