## Ou Zhao

In this talk I will quickly survey some recent progresses on the (conditional) central limit questions for stationary processes. One recent Markov chain example will be focused on, and its analysis is leading to some interesting phenomenon, which apparently we have not understood well yet. In vague terms, the partial sum of this Markov chain has variance growing faster than n, which delivers some challenge to prove the conditional CLT. But when we managed to show a CLT, it was found there is a `mass escaping' --- limiting variance