On the quenched central limit theorem for random dynamical systems

Journal Article
المجلة \ الصحيفة: 
Journal of Physics A: Mathematical and Theoretical
رقم العدد: 
24
رقم الإصدار السنوي: 
49
مستخلص المنشور: 

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