A central limit theorem for reversible processes with non-linear growth of variance

Ou Zhao, Michael Woodroofe, Dalibor Volny

Kipnis and Varadhan showed that for an additive functional, $S_n$ say, of a reversible Markov chain the condition $E(S_n^2)/n\to \kappa \in (0,\infty )$ implies the convergence of the…