How Long does it Take to Train an Elephant Random Walk
Abstract
Abstract We study how conditioning on the first k steps, which we think of as training, affects the long-term behavior of the Elephant Random Walk. When the elephant is conditioned to be at position k at time k , the first return time to the origin scales as $$k^{(4-4p)/(3-4p)}$$ k ( 4 - 4 p ) / ( 3 - 4 p ) in the diffusive regime, and grows exponentially in the critical regime. We loosely interpret this as a measurement of the rate at which the elephant forgets its training.
Fields of Study & Subjects
Theoretical and Computational Physics
stochastic dynamics and bifurcation
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Journal of Statistical Physics
- Volume
- 193
- Issue
- 7
- Pages
- 80–80
- Publication date
- 19 June 2026
- Language
- EN