Journal Article

FZJ-2018-00124

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Central limit theorem and related results for the elephant random walk

Coletti, C. F. ; Gava, R. ; Schütz, G. M. (Corresponding author)FZJ*

2017
American Inst. of Physics College Park, Md.

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Please use a persistent id in citations: http://hdl.handle.net/2128/16387  doi:10.1063/1.4983566

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

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Contributing Institute(s):

1. Theorie der Weichen Materie und Biophysik (ICS-2)

Research Program(s):

1. 551 - Functional Macromolecules and Complexes (POF3-551) (POF3-551)

Appears in the scientific report 2017

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Database coverage:
; ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; IF < 5 ; JCR ; Nationallizenz ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Thomson Reuters Master Journal List ; Web of Science Core Collection

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