A simple proof of a central limit theorem for stationary random fields under mixing conditions is given, generalizing some results obtained by more complicated methods, e.g. Bernstein's method.
"On the Central Limit Theorem for Stationary Mixing Random Fields." Ann. Probab. 10 (4) 1047 - 1050, November, 1982. https://doi.org/10.1214/aop/1176993726