Structures in random fields: Gaussian fields

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Abstract
We present two alternative methods for evaluating the probability densities of structures defined by d degrees of freedom in random fields. For Gaussian random fields, both differentiable and nondifferentiable, the application of these methods is considered in detail. The relationship between structures, maxima, and connected regions above a certain level is investigated. The connected correlation functions of these objects are expressed in terms of the autocorrelation of the field.

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