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Calculation of the distribution of the average value of a Gaussian randomfield in a finite domain is carried out for different cases. The results of thecalculation demonstrate a strong dependence of the width of the distribution onthe spatial correlations of the field. Comparison with the simulation resultsfor the distribution of the size of the cluster indicates that the distributionof an average field could serve as a useful tool for the estimation of theasymptotic behavior of the distribution of the size of the clusters for "deep"clusters where value of the field on each site is much greater than the rmsdisorder.

Distribution of averages in a correlated Gaussian medium as a tool for the estimation of the cluster distribution on size