We introduce a general method, which combines the one developed by authors in 1997 and one derived from the work of Malevich, Cuzick and mainly Berman, to provide in an easy way a CLT for level functionals of a Gaussian process, as well as a CLT for the length of a level curve of a Gaussian field.
KRATZ, M. et LEON, J. (2001). Central Limit Theorems for Level Functionals of Stationary Gaussian Processes and Fields. Journal of Theoretical Probability, 14(3), pp. 639-672.