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Asymptotic expansions for potential functions of I.I.D. random fields. (English) Zbl 0659.60035
For sums of finite range potential functions of an iid random field we derive the validity of formal expansions of length two. Under standard conditions, formal expansions are valid if and only if the characteristic functions of the sum converge to zero for all nonzero frequency parameters. If this convergence fails, the distribution of the sum can be approximated by a mixture of lattice distributions. The result applies to m-dependent random fields generated by independent random variables.
Reviewer: F.Götze

MSC:
60F05 Central limit and other weak theorems
60G60 Random fields
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