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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Central limit theorem and related results for the elephant random walk

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Author(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: 10
Abstract

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 type: Scholarships abroad - Research