Carol Bezuidenhout | University of Rochester - Estados Unidos
Self-similarity and the transition from finite to infinite measures in dynamical s...
Coletti, Cristian F. ; Gava, Renato ; Schuetz, Gunter M.
Total Authors: 3
|Document type:||Journal article|
|Source:||Journal of Mathematical Physics; v. 58, n. 5 MAY 2017.|
|Web of Science Citations:||14|
We study the so-called elephant random walk (ERW) which is a non-Markovian discrete-time random walk on Z with unbounded memory which exhibits a phase transition from a diffusive to superdiffusive behavior. We prove a law of large numbers and a central limit theorem. Remarkably the central limit theorem applies not only to the diffusive regime but also to the phase transition point which is superdiffusive. Inside the superdiffusive regime, the ERW converges to a non-degenerate random variable which is not normal. We also obtain explicit expressions for the correlations of increments of the ERW. Published by AIP Publishing. (AU)
|FAPESP's process:||15/20110-0 - Branching Random Walks and Interacting particle System in Random Environment.|
|Grantee:||Cristian Favio Coletti|
|Support Opportunities:||Scholarships abroad - Research|