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The central limit theorem for random fields. (English) Zbl 0801.60017
The author proves an appropriate version of the central limit theorem for random fields derived from the Gibbs distributions. The result obeys a natural interpretation of its assumptions. The approach is based on a general Rosenblatt’s theorem which is shown to be well suited to the case of Gibbs underlying distributions, whenever Dobrushin’s uniqueness condition is satisfied.
60F05 Central limit and other weak theorems
60G60 Random fields
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