On the quenched central limit theorem for random dynamical systems. (6th May 2016)

• Record Type: Journal Article
• Authors: Abdelkader, Mohamed; Aimino, Romain
• Is Part Of: Journal of physics. Volume 49:Number 24(2016)
• Publication Date: 2016-05-06
• Subjects: random dynamical systems -- quenched limit theorems -- central limit theorem -- transfer operators; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/24/244002
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We provide a necessary and sufficient condition under which the quenched central limit theorem without random centering holds for one-dimensional random systems that are uniformly expanding. This condition holds in particular when all the maps preserve a common measure. We also give a counter example which shows that this condition is not necessarily satisfied when the maps do not preserve a common measure.