Limits theorems for random walks on homeo\(( \mathrm{S}^1)\) (Q2116526)

This work studies random walks on the circle, with transitions given by random homeomorphisms. The main results are a central limit theorem and a law of iterated logarithm. More precisely, these results had been established in previous works for almost all initial conditions, and this work extends them to all initial conditions. The extension is based on an almost sure contraction of intervals along the transitions of the chain.