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A reduction theorem is proved for functionals of Gamma-correlated randomfields with long-range dependence in d-dimensional space. In the particularcase of a non-linear function of a chi-squared random field with Laguerre rankequal to one, we apply the Karhunen-Lo\'eve expansion and the Fredholmdeterminant formula to obtain the characteristic function of itsRosenblatt-type limit distribution. When the Laguerre rank equals one and two,we obtain the multiple Wiener-It\^o stochastic integral representation of thelimit distribution. In both cases, an infinite series representation in termsof independent random variables is constructed for the limit random variables.

Non-central limit theorems for random fields subordinated to gamma-correlated random fields