Abstract: We provide a classification of random orientation-preserving homeomorphisms of the circle, up to topological conjugacy of the random dynamical systems generated by i.i.d. iterates. This classification concerns random circle homeomorphisms for which the noise space is a connected Polish space and some other minor conditions are satisfied.

This is joint work with Thai Son Doan (Vietnam Academy of Sciences), Julian Newman (Lancaster University) and Martin Rasmussen (Imperial College London).