Realisability conditions for second order marginals of biphased media

Abstract : This paper concerns the second order marginals of biphased random media. We give discriminating necessary conditions for a bivariate function to be such a valid marginal, and illustrate our study with two practical applications: (1) the spherical variograms are valid indicator variograms if and only if they are multiplied by a sufficiently small constant, which upper bound is estimated, and (2) not every covariance/indicator variogram can be obtained with a Gaussian level set. The theoretical results backing this study are contained in a companion paper.
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Random Structures and Algorithms, Wiley, 2015, 47 (3), pp.588-604. 〈http://onlinelibrary.wiley.com/doi/10.1002/rsa.20546/abstract〉. 〈10.1002/rsa.20546〉
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Raphaël Lachièze-Rey. Realisability conditions for second order marginals of biphased media. Random Structures and Algorithms, Wiley, 2015, 47 (3), pp.588-604. 〈http://onlinelibrary.wiley.com/doi/10.1002/rsa.20546/abstract〉. 〈10.1002/rsa.20546〉. 〈hal-00799443〉

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